diff --git a/build/doctrees/course-info/exam.doctree b/build/doctrees/course-info/exam.doctree
index 663a8c5..7ef7ad1 100644
Binary files a/build/doctrees/course-info/exam.doctree and b/build/doctrees/course-info/exam.doctree differ
diff --git a/build/doctrees/environment.pickle b/build/doctrees/environment.pickle
index 1cf4314..861c5e7 100644
Binary files a/build/doctrees/environment.pickle and b/build/doctrees/environment.pickle differ
diff --git a/build/html/_sources/course-info/exam.rst.txt b/build/html/_sources/course-info/exam.rst.txt
index 6546056..5aad795 100644
--- a/build/html/_sources/course-info/exam.rst.txt
+++ b/build/html/_sources/course-info/exam.rst.txt
@@ -31,7 +31,7 @@ Grading: Notebooks will be graded based on:
 - quality of the plots (axis labels, readability of the labels)
 - use of concepts we used for the notebooks (use of markdown, multiple code cells )
 
-The deadline for handing in the project is **September 4, 2024** 
+The deadline for handing in the project is **September 4, 2024, at 1pm sharp! Do not miss the deadline!!!!!!**
 
 Please submit your projects via email to Andrea Kramer,  **firstname.surname@uni-leipzig.de**.
 
diff --git a/build/html/course-info/exam.html b/build/html/course-info/exam.html
index 80daa68..8f5cede 100644
--- a/build/html/course-info/exam.html
+++ b/build/html/course-info/exam.html
@@ -237,7 +237,7 @@ <h1>Exam<a class="headerlink" href="#exam" title="Permalink to this heading">#</
 <li><p>quality of the plots (axis labels, readability of the labels)</p></li>
 <li><p>use of concepts we used for the notebooks (use of markdown, multiple code cells )</p></li>
 </ul>
-<p>The deadline for handing in the project is <strong>September 4, 2024</strong></p>
+<p>The deadline for handing in the project is <strong>September 4, 2024, at 1pm sharp! Do not miss the deadline!!!!!!</strong></p>
 <p>Please submit your projects via email to Andrea Kramer,  <strong>firstname.surname&#64;uni-leipzig.de</strong>.</p>
 <p>Since many of you asked for some guiding topics and I as well hope that you do not submit a simulation of planetary motion, here are some topics, though some of them might be for the advanced physicist.</p>
 <section id="mechanics">
diff --git a/build/html/searchindex.js b/build/html/searchindex.js
index 1041b48..9087e62 100644
--- a/build/html/searchindex.js
+++ b/build/html/searchindex.js
@@ -1 +1 @@
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"Data-Types-in-Python"], [47, "Data-Types-in-Python"]], "Strings": [[45, "Strings"], [47, "Strings"]], "Lists": [[45, "Lists"], [47, "Lists"]], "Tuples": [[45, "Tuples"], [47, "Tuples"]], "Dictionaries": [[45, "Dictionaries"], [47, "Dictionaries"]], "Sets": [[45, "Sets"]], "Modules and namespaces": [[46, "Modules-and-namespaces"]], "Modules": [[46, "Modules"], [47, "Modules"]], "Namespaces": [[46, "Namespaces"]], "Contents of a module": [[46, "Contents-of-a-module"]], "Type casting": [[47, "Type-casting"]], "Contents and documentation of a module": [[47, "Contents-and-documentation-of-a-module"]], "Exceptions": [[47, "Exceptions"], [48, "Exceptions"], [73, "Exceptions"]], "What\u2019s next": [[47, "What's-next"]], "Quantum Mechanics": [[49, "Quantum-Mechanics"], [5, "quantum-mechanics"]], "Quantum Mechanics in a Nutshell": [[49, "Quantum-Mechanics-in-a-Nutshell"]], "Time dependent Schr\u00f6dinger equation": [[49, "Time-dependent-Schr\u00f6dinger-equation"], [53, "Time-dependent-Schr\u00f6dinger-equation"]], "Stationary Schr\u00f6dinger equation": [[49, "Stationary-Schr\u00f6dinger-equation"]], "Recap: Implicit Solution": [[49, "Recap:-Implicit-Solution"]], "Kinetic energy": [[49, "Kinetic-energy"], [50, "Kinetic-energy"], [51, "Kinetic-energy"], [52, "Kinetic-energy"]], "Potential energy": [[49, "Potential-energy"], [50, "Potential-energy"], [51, "Potential-energy"], [52, "Potential-energy"]], "Particle in a box": [[50, "Particle-in-a-box"]], "Definition of the problem": [[50, "Definition-of-the-problem"], [51, "Definition-of-the-problem"], [52, "Definition-of-the-problem"]], "Solution": [[50, "Solution"], [51, "Solution"], [52, "Solution"], [81, "Solution"], [81, "id1"], [81, "id4"], [83, "Solution"], [87, "Solution"], [89, "Solution"]], "Plotting": [[50, "Plotting"], [51, "Plotting"], [52, "Plotting"], [81, "Plotting"], [81, "id5"], [83, "Plotting"], [84, "Plotting"], [87, "Plotting"]], "Energies of bound states": [[50, "Energies-of-bound-states"]], "Where to go from here?": [[50, "Where-to-go-from-here?"], [51, "Where-to-go-from-here?"], [52, "Where-to-go-from-here?"], [54, "Where-to-go-from-here?"], [55, "Where-to-go-from-here?"], [61, "Where-to-go-from-here?"]], "Harmonic Oscillator": [[51, "Harmonic-Oscillator"], [81, "Harmonic-Oscillator"]], "Energies of the states": [[51, "Energies-of-the-states"]], "Periodic Potential": [[52, "Periodic-Potential"]], "Energy states": [[52, "Energy-states"]], "Time Dependent Quantum Mechanics": [[53, "Time-Dependent-Quantum-Mechanics"]], "Wavepackets": [[53, "Wavepackets"]], "Demonstration of superposition of plane waves": [[53, "Demonstration-of-superposition-of-plane-waves"]], "Wavepacket": [[53, "Wavepacket"]], "Wavepacket with rectangular amplitude": [[53, "Wavepacket-with-rectangular-amplitude"]], "Gaussian Wave Packet": [[53, "Gaussian-Wave-Packet"]], "Time evolution of a Gaussian Wavepacket": [[53, "Time-evolution-of-a-Gaussian-Wavepacket"]], "Wavepacket in a Potential Box": [[54, "Wavepacket-in-a-Potential-Box"]], "Problem Setup": [[54, "Problem-Setup"]], "Initial conditions": [[54, "Initial-conditions"]], "Eigenfunctions": [[54, "Eigenfunctions"]], "Quality of the coefficients": [[54, "Quality-of-the-coefficients"]], "Animation": [[54, "Animation"], [55, "Animation"], [55, "id3"], [84, "Animation"], [92, "Animation"], [93, "Animation"], [95, "Animation"]], "Tunneling through a barrier": [[55, "Tunneling-through-a-barrier"]], "Schr\u00f6dinger equation for the momentum": [[55, "Schr\u00f6dinger-equation-for-the-momentum"]], "Crank Nicolson Solution": [[55, "Crank-Nicolson-Solution"]], "Setup Domain": [[55, "Setup-Domain"], [55, "id1"], [89, "Setup-Domain"]], "Initial Conditions": [[55, "Initial-Conditions"], [57, "Initial-Conditions"], [89, "Initial-Conditions"]], "Matrix Setup": [[55, "Matrix-Setup"], [89, "Matrix-Setup"]], "Propagation Matrix": [[55, "Propagation-Matrix"]], "Animation setup": [[55, "Animation-setup"], [55, "id2"]], "Split Step Method": [[55, "Split-Step-Method"], [56, "Split-Step-Method"]], "Potential energy landscape": [[55, "Potential-energy-landscape"]], "Initial wavepacket": [[55, "Initial-wavepacket"]], "Fourier Transform Setup": [[55, "Fourier-Transform-Setup"]], "Phase Factor per Timestep": [[55, "Phase-Factor-per-Timestep"]], "Old Split Step Method": [[56, "Old-Split-Step-Method"]], "Setup the simulation": [[56, "Setup-the-simulation"]], "Hydrodynamics": [[57, "Hydrodynamics"]], "Falling sphere": [[57, "Falling-sphere"]], "Setup": [[57, "Setup"], [81, "Setup"], [81, "id2"], [83, "Setup"]], "Function definition": [[57, "Function-definition"], [72, "Function-definition"]], "Numerical solution": [[57, "Numerical-solution"]], "Analytical solution": [[57, "Analytical-solution"]], "Stokes equation": [[57, "Stokes-equation"]], "Fundamental Solutions of the Stokes Equation": [[57, "Fundamental-Solutions-of-the-Stokes-Equation"]], "Stokeslet": [[57, "Stokeslet"]], "Source dipole": [[57, "Source-dipole"]], "Sum of both solutions": [[57, "Sum-of-both-solutions"]], "Machine Learning and Neural Networks": [[58, "Machine-Learning-and-Neural-Networks"]], "Reinforcement Learning": [[58, "Reinforcement-Learning"]], "Markov Decision Process": [[58, "Markov-Decision-Process"]], "Methods or RL": [[58, "Methods-or-RL"]], "Navigating a Grid World": [[58, "Navigating-a-Grid-World"]], "Initialize Reinforcement Learning": [[58, "Initialize-Reinforcement-Learning"]], "List of actions": [[58, "List-of-actions"]], "Initial state": [[58, "Initial-state"]], "Reinforcement Learning Loop": [[58, "Reinforcement-Learning-Loop"]], "Convergence of the Q-learning": [[58, "Convergence-of-the-Q-learning"]], "Policy": [[58, "Policy"]], "Plot the policy": [[58, "Plot-the-policy"]], "Where to go from here": [[58, "Where-to-go-from-here"]], "Neural Networks": [[59, "Neural-Networks"]], "The MNIST Data Set": [[59, "The-MNIST-Data-Set"]], "Load the data": [[59, "Load-the-data"]], "Normalize the data": [[59, "Normalize-the-data"]], "Preparing training and testing data": [[59, "Preparing-training-and-testing-data"]], "A Single Neuron": [[59, "A-Single-Neuron"]], "Forward Propogation": [[59, "Forward-Propogation"]], "Loss Function": [[59, "Loss-Function"], [59, "id1"]], "Trainging the Network": [[59, "Trainging-the-Network"]], "Backward Propagation": [[59, "Backward-Propagation"]], "Stochastic Gradient Descent": [[59, "Stochastic-Gradient-Descent"]], "Build an Train": [[59, "Build-an-Train"]], "Testing our model": [[59, "Testing-our-model"]], "Network with Hidden Layers": [[59, "Network-with-Hidden-Layers"]], "Multiclass Network": [[59, "Multiclass-Network"]], "Changes to the model": [[59, "Changes-to-the-model"]], "Forward Pass": [[59, "Forward-Pass"]], "Back Propagation": [[59, "Back-Propagation"]], "Build and Train": [[59, "Build-and-Train"]], "Model performance": [[59, "Model-performance"]], "Test the model": [[59, "Test-the-model"]], "Neural Network with Keras": [[60, "Neural-Network-with-Keras"]], "MNIST Data Set (Keras)": [[60, "MNIST-Data-Set-(Keras)"]], "Build the model": [[60, "Build-the-model"]], "Compile the model": [[60, "Compile-the-model"]], "Train the model": [[60, "Train-the-model"]], "Testing the model": [[60, "Testing-the-model"]], "Convolutional Neural Networks": [[61, "Convolutional-Neural-Networks"]], "Layout of a CNN": [[61, "Layout-of-a-CNN"]], "Convolutional Layer": [[61, "Convolutional-Layer"]], "Padding": [[61, "Padding"]], "Striding": [[61, "Striding"]], "RELU Activation": [[61, "RELU-Activation"]], "Pooling Layer": [[61, "Pooling-Layer"]], "Output Size": [[61, "Output-Size"]], "Flattening": [[61, "Flattening"]], "Dropout": [[61, "Dropout"]], "Fully Connected Layer": [[61, "Fully-Connected-Layer"]], "Example CNN with Keras": [[61, "Example-CNN-with-Keras"]], "Prepare the data": [[61, "Prepare-the-data"]], "Build the network": [[61, "Build-the-network"]], "Train the network": [[61, "Train-the-network"]], "Evaluate the trained network": [[61, "Evaluate-the-trained-network"]], "Evaluate the accuracy of your visual neural network ;-)": [[61, "Evaluate-the-accuracy-of-your-visual-neural-network-;-)"]], "Autoencoder CNN for Time Series Denoising": [[62, "Autoencoder-CNN-for-Time-Series-Denoising"]], "Autoencoder Structure and Purpose": [[62, "Autoencoder-Structure-and-Purpose"]], "Data Generation": [[62, "Data-Generation"]], "Create the Autoencoder network": [[62, "Create-the-Autoencoder-network"]], "Define model data": [[62, "Define-model-data"]], "Encoder/Decoder Setup": [[62, "Encoder/Decoder-Setup"]], "Training the encoder": [[62, "Training-the-encoder"]], "Reconstruction of the Data": [[62, "Reconstruction-of-the-Data"]], "Python and Hardware": [[63, "Python-and-Hardware"]], "Arduino Nano Board": [[63, "Arduino-Nano-Board"]], "Arduino Software": [[63, "Arduino-Software"]], "Setup your board": [[63, "Setup-your-board"]], "Select Firmata Sketch": [[63, "Select-Firmata-Sketch"]], "Communicating with the board": [[63, "Communicating-with-the-board"]], "Let the on-board LED blink": [[63, "Let-the-on-board-LED-blink"]], "Tunable output": [[63, "Tunable-output"]], "Creating an Oscilloscope": [[63, "Creating-an-Oscilloscope"]], "Project: YOUR PROJECT TITLE": [[64, "Project:-YOUR-PROJECT-TITLE"]], "Introduction": [[64, "Introduction"]], "Fundamentals": [[64, "Fundamentals"]], "Results and Discussion": [[64, "Results-and-Discussion"]], "Summary": [[64, "Summary"]], "NumPy arrays": [[65, "NumPy-arrays"]], "Creating Numpy Arrays": [[65, "Creating-Numpy-Arrays"]], "From lists": [[65, "From-lists"]], "Using array-generating functions": [[65, "Using-array-generating-functions"]], "linspace and logspace": [[65, "linspace-and-logspace"]], "mgrid": [[65, "mgrid"]], "diag": [[65, "diag"]], "zeros and ones": [[65, "zeros-and-ones"]], "Manipulating NumPy arrays": [[65, "Manipulating-NumPy-arrays"]], "Slicing": [[65, "Slicing"]], "Reshaping": [[65, "Reshaping"]], "Adding a new dimension: newaxis": [[65, "Adding-a-new-dimension:-newaxis"]], "Stacking and repeating arrays": [[65, "Stacking-and-repeating-arrays"]], "Tile and repeat": [[65, "Tile-and-repeat"]], "Concatenate": [[65, "Concatenate"]], "Hstack and vstack": [[65, "Hstack-and-vstack"]], "Applying mathematical functions": [[65, "Applying-mathematical-functions"]], "Operation involving one array": [[65, "Operation-involving-one-array"]], "Operations involving multiple arrays": [[65, "Operations-involving-multiple-arrays"]], "Add On: Making publication ready figures": [[66, "Add-On:-Making-publication-ready-figures"]], "Creating a plot with a specific bounding box size": [[66, "Creating-a-plot-with-a-specific-bounding-box-size"]], "Creating a plot with a specific axis frame size": [[66, "Creating-a-plot-with-a-specific-axis-frame-size"]], "Choosing fonts": [[66, "Choosing-fonts"]], "Plotting data": [[67, "Plotting-data"]], "Simple Plotting - Implicit Version": [[67, "Simple-Plotting---Implicit-Version"]], "Line Plot": [[67, "Line-Plot"]], "Axis Labels": [[67, "Axis-Labels"]], "Legends": [[67, "Legends"]], "Scatter plot": [[67, "Scatter-plot"]], "Histograms": [[67, "Histograms"]], "Combined plots": [[67, "Combined-plots"]], "Saving figures": [[67, "Saving-figures"]], "Plots with error bars": [[67, "Plots-with-error-bars"]], "Setting plotting limits and excluding data": [[67, "Setting-plotting-limits-and-excluding-data"]], "Masked arrays": [[67, "Masked-arrays"]], "Logarithmic plots": [[67, "Logarithmic-plots"]], "Semi-log plots": [[67, "Semi-log-plots"]], "Log-log plots": [[67, "Log-log-plots"]], "Arranging multiple plots": [[67, "Arranging-multiple-plots"]], "Contour and Density Plots": [[67, "Contour-and-Density-Plots"]], "Simple contour plot": [[67, "Simple-contour-plot"]], "Color contour plot": [[67, "Color-contour-plot"]], "Image plot": [[67, "Image-plot"]], "Additional Plotting - Explicit Version": [[67, "Additional-Plotting---Explicit-Version"]], "Plots with Multiple Spines": [[67, "Plots-with-Multiple-Spines"]], "Insets": [[67, "Insets"]], "Spine axis": [[67, "Spine-axis"]], "Polar plot": [[67, "Polar-plot"]], "Text annotation": [[67, "Text-annotation"]], "3D Plotting": [[67, "3D-Plotting"]], "Projection Scence": [[67, "Projection-Scence"]], "Line Plotting in 3D": [[67, "Line-Plotting-in-3D"]], "Surface Plotting": [[67, "Surface-Plotting"]], "Random numbers": [[68, "Random-numbers"]], "Uniformly distributed random numbers": [[68, "Uniformly-distributed-random-numbers"]], "Normally distributed random numbers": [[68, "Normally-distributed-random-numbers"]], "Exponentially distributed numbers": [[68, "Exponentially-distributed-numbers"]], "Random distribution of integers": [[68, "Random-distribution-of-integers"]], "Problem Set 2": [[69, "Problem-Set-2"]], "Input and output": [[70, "Input-and-output"]], "Keyboard input": [[70, "Keyboard-input"]], "Screen output": [[70, "Screen-output"]], "str.format() Formatting": [[70, "str.format()-Formatting"]], "%-Formatting": [[70, "%-Formatting"]], "f-Strings": [[70, "f-Strings"]], "File input/output": [[70, "File-input/output"]], "File I/O with NumPy": [[70, "File-I/O-with-NumPy"]], "Reading data from a text file": [[70, "Reading-data-from-a-text-file"]], "Writing data to a text file": [[70, "Writing-data-to-a-text-file"]], "File I/O with Pandas": [[70, "File-I/O-with-Pandas"]], "Short intro to Pandas": [[70, "Short-intro-to-Pandas"]], "Reading CSV data with Pandas": [[70, "Reading-CSV-data-with-Pandas"]], "Conditionals: if, elif, and else statements": [[71, "Conditionals:-if,-elif,-and-else-statements"]], "If example": [[71, "If-example"]], "If else example": [[71, "If-else-example"]], "If, elif, else example": [[71, "If,-elif,-else-example"]], "Combining conditions": [[71, "Combining-conditions"]], "For loops": [[71, "For-loops"]], "While loops": [[71, "While-loops"]], "Loops and array operations": [[71, "Loops-and-array-operations"], [74, "Loops-and-array-operations"]], "List comprehensions": [[71, "List-comprehensions"]], "Variables in functions": [[72, "Variables-in-functions"]], "Functions with more than one input or output": [[72, "Functions-with-more-than-one-input-or-output"], [74, "Functions-with-more-than-one-input-or-output"]], "Positional and keyword arguments": [[72, "Positional-and-keyword-arguments"], [74, "Positional-and-keyword-arguments"]], "Functions with variable number of arguments": [[72, "Functions-with-variable-number-of-arguments"]], "Unnamed functions (lambda function)": [[72, "Unnamed-functions-(lambda-function)"]], "Functions as arguments of functions": [[72, "Functions-as-arguments-of-functions"]], "Introduction to Computational Software": [[74, "Introduction-to-Computational-Software"]], "Table of Contents": [[74, "Table-of-Contents"]], "Lecture 3": [[74, "Lecture-3"]], "Conditionals": [[74, "Conditionals"]], "if, elif, and else statements": [[74, "if,-elif,-and-else-statements"]], "Logical Operators": [[74, "Logical-Operators"]], "for loops": [[74, "for-loops"]], "while loops": [[74, "while-loops"]], "List Comprehensions": [[74, "List-Comprehensions"]], "User-defined functions": [[74, "User-defined-functions"]], "Faster Array Processing": [[74, "Faster-Array-Processing"]], "Variable number of arguments": [[74, "Variable-number-of-arguments"]], "Numerical differentiation": [[74, "Numerical-differentiation"]], "More differentiation": [[74, "More-differentiation"]], "Classes and Objects": [[76, "Classes-and-Objects"]], "Definition of Classes": [[76, "Definition-of-Classes"]], "Class Methods": [[76, "Class-Methods"]], "The __init__ method": [[76, "The-__init__-method"]], "The __str__ method": [[76, "The-__str__-method"]], "Class and object variables": [[76, "Class-and-object-variables"]], "Brownian Motion": [[77, "Brownian-Motion"]], "Physics": [[77, "Physics"]], "Class Planning": [[77, "Class-Planning"]], "Simulating": [[77, "Simulating"]], "Plotting the trajectories": [[77, "Plotting-the-trajectories"]], "Characterizing the Brownian motion": [[77, "Characterizing-the-Brownian-motion"]], "Calculate the particle speed": [[77, "Calculate-the-particle-speed"]], "Calculate the particle mean squared displacement": [[77, "Calculate-the-particle-mean-squared-displacement"]], "Animations": [[78, "Animations"]], "Import Modules": [[78, "Import-Modules"]], "Particle class": [[78, "Particle-class"]], "Create a set of particles": [[78, "Create-a-set-of-particles"]], "Canvas and drawing function": [[78, "Canvas-and-drawing-function"]], "Threading for animation": [[78, "Threading-for-animation"]], "Numerical Differentiation": [[79, "Numerical-Differentiation"]], "First order derivative": [[79, "First-order-derivative"]], "Matrix version of the first derivative": [[79, "Matrix-version-of-the-first-derivative"]], "Second order derivative": [[79, "Second-order-derivative"]], "SciPy Module": [[79, "SciPy-Module"]], "Matrix version": [[79, "Matrix-version"]], "Numerical Integration": [[80, "Numerical-Integration"]], "Box method": [[80, "Box-method"]], "Trapezoid method": [[80, "Trapezoid-method"]], "Simpson method": [[80, "Simpson-method"]], "Solving ODEs": [[81, "Solving-ODEs"]], "Implicit Solution - Crank Nicholson": [[81, "Implicit-Solution---Crank-Nicholson"]], "Define Matrices": [[81, "Define-Matrices"]], "Use Initial Conditions": [[81, "Use-Initial-Conditions"]], "Explicit Solution - Numerical Integration": [[81, "Explicit-Solution---Numerical-Integration"]], "Euler Method": [[81, "Euler-Method"]], "Euler Cromer Method": [[81, "Euler-Cromer-Method"]], "Midpoint Method": [[81, "Midpoint-Method"]], "Putting it all together": [[81, "Putting-it-all-together"]], "The definition of the problem": [[81, "The-definition-of-the-problem"]], "Solving the problem": [[81, "Solving-the-problem"], [84, "Solving-the-problem"]], "Solving the Harmonic Oscillator in SciPy": [[81, "Solving-the-Harmonic-Oscillator-in-SciPy"]], "Definition": [[81, "Definition"], [81, "id3"], [83, "Definition"]], "Damped Driven Pendulum in SciPy": [[81, "Damped-Driven-Pendulum-in-SciPy"]], "Utilities": [[82, "Utilities"]], "COVID19": [[83, "COVID19"]], "The Kermack-McKendrick Model": [[83, "The-Kermack-McKendrick-Model"]], "Model Equation": [[83, "Model-Equation"]], "Real COVID19 numbers": [[83, "Real-COVID19-numbers"]], "Total number of cases": [[83, "Total-number-of-cases"]], "Number of Deaths": [[83, "Number-of-Deaths"]], "New cases per day": [[83, "New-cases-per-day"]], "Current cases": [[83, "Current-cases"]], "Coupled Pendula": [[84, "Coupled-Pendula"]], "Description of the problem": [[84, "Description-of-the-problem"]], "Sketch": [[84, "Sketch"]], "Equations of motion": [[84, "Equations-of-motion"], [87, "Equations-of-motion"]], "Setting up the function": [[84, "Setting-up-the-function"]], "Define initial parameters": [[84, "Define-initial-parameters"]], "Solve the equation of motion": [[84, "Solve-the-equation-of-motion"]], "Normal Modes": [[84, "Normal-Modes"]], "In-phase motion": [[84, "In-phase-motion"]], "Out-of-phase motion": [[84, "Out-of-phase-motion"]], "Beat case": [[84, "Beat-case"]], "Computation of energy (here for the beat case)": [[84, "Computation-of-energy-(here-for-the-beat-case)"]], "Potential energy of the pendula": [[84, "Potential-energy-of-the-pendula"]], "Potential energy of the spring": [[84, "Potential-energy-of-the-spring"]], "Kinetic energies": [[84, "Kinetic-energies"]], "Total energy": [[84, "Total-energy"]], "Total energy exchange of the pendula": [[84, "Total-energy-exchange-of-the-pendula"]], "Fourier Analysis": [[85, "Fourier-Analysis"]], "Fourier series": [[85, "Fourier-series"]], "Fourier transform": [[85, "Fourier-transform"]], "Frequency analysis of our coupled pendula": [[85, "Frequency-analysis-of-our-coupled-pendula"]], "Appendix: Fourier Analysis of a damped oscillation": [[86, "Appendix:-Fourier-Analysis-of-a-damped-oscillation"]], "Spring Pendulum": [[87, "Spring-Pendulum"]], "Physical Model": [[87, "Physical-Model"], [88, "Physical-Model"], [89, 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Contents": [[14, "lecture-contents"], [15, "lecture-contents"], [16, "lecture-contents"], [17, "lecture-contents"], [18, "lecture-contents"], [19, "lecture-contents"], [20, "lecture-contents"], [23, "lecture-contents"], [25, "lecture-contents"], [27, "lecture-contents"], [28, "lecture-contents"], [30, "lecture-contents"], [32, "lecture-contents"], [34, "lecture-contents"], [35, "lecture-contents"], [37, "lecture-contents"]], "Creating a figure, which just looks nice on the screen": [[21, "Creating-a-figure,-which-just-looks-nice-on-the-screen"]], "Creating a figure, which looks good in paper and on screen": [[21, "Creating-a-figure,-which-looks-good-in-paper-and-on-screen"]], "Exercise 2": [[22, "exercise-2"]], "Exercise 3": [[24, "exercise-3"]], "Exercise 4": [[26, "exercise-4"]], "Exercise 5": [[29, "exercise-5"]], "Exercise 6": [[33, "exercise-6"]], "Exercise 7": [[36, "exercise-7"], [31, "exercise-7"]], "Entering code": [[40, "Entering-code"]], "Entering Markdown": [[40, "Entering-Markdown"]], "Markdown basics": [[40, "Markdown-basics"]], "Headings": [[40, "Headings"]], "Embedded code": [[40, "Embedded-code"]], "LaTeX equations": [[40, "LaTeX-equations"]], "Images": [[40, "Images"]], "Videos": [[40, "Videos"]], "An empty notebook": [[41, "An-empty-notebook"]], "Variables and types": [[43, "Variables-and-types"], [47, "Variables-and-types"]], "Symbol names": [[43, "Symbol-names"], [47, "Symbol-names"]], "Variable Assignment": [[43, "Variable-Assignment"], [47, "Variable-Assignment"]], "Number types": [[43, "Number-types"], [47, "Number-types"]], "Integers": [[43, "Integers"], [47, "Integers"]], "Floating Point": [[43, "Floating-Point"], [47, "Floating-Point"]], "Complex Numbers": [[43, "Complex-Numbers"], [47, "Complex-Numbers"]], "Type conversion": [[43, "Type-conversion"]], "Operators and comparisons": [[44, "Operators-and-comparisons"], [47, "Operators-and-comparisons"]], "Data Types in Python": [[45, "Data-Types-in-Python"], [47, "Data-Types-in-Python"]], "Strings": [[45, "Strings"], [47, "Strings"]], "Lists": [[45, "Lists"], [47, "Lists"]], "Tuples": [[45, "Tuples"], [47, "Tuples"]], "Dictionaries": [[45, "Dictionaries"], [47, "Dictionaries"]], "Sets": [[45, "Sets"]], "Modules and namespaces": [[46, "Modules-and-namespaces"]], "Modules": [[46, "Modules"], [47, "Modules"]], "Namespaces": [[46, "Namespaces"]], "Contents of a module": [[46, "Contents-of-a-module"]], "Type casting": [[47, "Type-casting"]], "Contents and documentation of a module": [[47, "Contents-and-documentation-of-a-module"]], "Exceptions": [[47, "Exceptions"], [48, "Exceptions"], [73, "Exceptions"]], "What\u2019s next": [[47, "What's-next"]], "Quantum Mechanics": [[49, "Quantum-Mechanics"], [5, "quantum-mechanics"]], "Quantum Mechanics in a Nutshell": [[49, "Quantum-Mechanics-in-a-Nutshell"]], "Time dependent Schr\u00f6dinger equation": [[49, "Time-dependent-Schr\u00f6dinger-equation"], [53, "Time-dependent-Schr\u00f6dinger-equation"]], "Stationary Schr\u00f6dinger equation": [[49, "Stationary-Schr\u00f6dinger-equation"]], "Recap: Implicit Solution": [[49, "Recap:-Implicit-Solution"]], "Kinetic energy": [[49, "Kinetic-energy"], [50, "Kinetic-energy"], [51, "Kinetic-energy"], [52, "Kinetic-energy"]], "Potential energy": [[49, "Potential-energy"], [50, "Potential-energy"], [51, "Potential-energy"], [52, "Potential-energy"]], "Particle in a box": [[50, "Particle-in-a-box"]], "Definition of the problem": [[50, "Definition-of-the-problem"], [51, "Definition-of-the-problem"], [52, "Definition-of-the-problem"]], "Solution": [[50, "Solution"], [51, "Solution"], [52, "Solution"], [81, "Solution"], [81, "id1"], [81, "id4"], [83, "Solution"], [87, "Solution"], [89, "Solution"]], "Plotting": [[50, "Plotting"], [51, "Plotting"], [52, "Plotting"], [81, "Plotting"], [81, "id5"], [83, "Plotting"], [84, "Plotting"], [87, "Plotting"]], "Energies of bound states": [[50, "Energies-of-bound-states"]], "Where to go from here?": [[50, "Where-to-go-from-here?"], [51, "Where-to-go-from-here?"], [52, "Where-to-go-from-here?"], [54, "Where-to-go-from-here?"], [55, "Where-to-go-from-here?"], [61, "Where-to-go-from-here?"]], "Harmonic Oscillator": [[51, "Harmonic-Oscillator"], [81, "Harmonic-Oscillator"]], "Energies of the states": [[51, "Energies-of-the-states"]], "Periodic Potential": [[52, "Periodic-Potential"]], "Energy states": [[52, "Energy-states"]], "Time Dependent Quantum Mechanics": [[53, "Time-Dependent-Quantum-Mechanics"]], "Wavepackets": [[53, "Wavepackets"]], "Demonstration of superposition of plane waves": [[53, "Demonstration-of-superposition-of-plane-waves"]], "Wavepacket": [[53, "Wavepacket"]], "Wavepacket with rectangular amplitude": [[53, "Wavepacket-with-rectangular-amplitude"]], "Gaussian Wave Packet": [[53, "Gaussian-Wave-Packet"]], "Time evolution of a Gaussian Wavepacket": [[53, "Time-evolution-of-a-Gaussian-Wavepacket"]], "Wavepacket in a Potential Box": [[54, "Wavepacket-in-a-Potential-Box"]], "Problem Setup": [[54, "Problem-Setup"]], "Initial conditions": [[54, "Initial-conditions"]], "Eigenfunctions": [[54, "Eigenfunctions"]], "Quality of the coefficients": [[54, "Quality-of-the-coefficients"]], "Animation": [[54, "Animation"], [55, "Animation"], [55, "id3"], [84, "Animation"], [92, "Animation"], [93, "Animation"], [95, "Animation"]], "Tunneling through a barrier": [[55, "Tunneling-through-a-barrier"]], "Schr\u00f6dinger equation for the momentum": [[55, "Schr\u00f6dinger-equation-for-the-momentum"]], "Crank Nicolson Solution": [[55, "Crank-Nicolson-Solution"]], "Setup Domain": [[55, "Setup-Domain"], [55, "id1"], [89, "Setup-Domain"]], "Initial Conditions": [[55, "Initial-Conditions"], [57, "Initial-Conditions"], [89, "Initial-Conditions"]], "Matrix Setup": [[55, "Matrix-Setup"], [89, "Matrix-Setup"]], "Propagation Matrix": [[55, "Propagation-Matrix"]], "Animation setup": [[55, "Animation-setup"], [55, "id2"]], "Split Step Method": [[55, "Split-Step-Method"], [56, "Split-Step-Method"]], "Potential energy landscape": [[55, "Potential-energy-landscape"]], "Initial wavepacket": [[55, "Initial-wavepacket"]], "Fourier Transform Setup": [[55, "Fourier-Transform-Setup"]], "Phase Factor per Timestep": [[55, "Phase-Factor-per-Timestep"]], "Old Split Step Method": [[56, "Old-Split-Step-Method"]], "Setup the simulation": [[56, "Setup-the-simulation"]], "Hydrodynamics": [[57, "Hydrodynamics"]], "Falling sphere": [[57, "Falling-sphere"]], "Setup": [[57, "Setup"], [81, "Setup"], [81, "id2"], [83, "Setup"]], "Function definition": [[57, "Function-definition"], [72, "Function-definition"]], "Numerical solution": [[57, "Numerical-solution"]], "Analytical solution": [[57, "Analytical-solution"]], "Stokes equation": [[57, "Stokes-equation"]], "Fundamental Solutions of the Stokes Equation": [[57, "Fundamental-Solutions-of-the-Stokes-Equation"]], "Stokeslet": [[57, "Stokeslet"]], "Source dipole": [[57, "Source-dipole"]], "Sum of both solutions": [[57, "Sum-of-both-solutions"]], "Machine Learning and Neural Networks": [[58, "Machine-Learning-and-Neural-Networks"]], "Reinforcement Learning": [[58, "Reinforcement-Learning"]], "Markov Decision Process": [[58, "Markov-Decision-Process"]], "Methods or RL": [[58, "Methods-or-RL"]], "Navigating a Grid World": [[58, "Navigating-a-Grid-World"]], "Initialize Reinforcement Learning": [[58, "Initialize-Reinforcement-Learning"]], "List of actions": [[58, "List-of-actions"]], "Initial state": [[58, "Initial-state"]], "Reinforcement Learning Loop": [[58, "Reinforcement-Learning-Loop"]], "Convergence of the Q-learning": [[58, "Convergence-of-the-Q-learning"]], "Policy": [[58, "Policy"]], "Plot the policy": [[58, "Plot-the-policy"]], "Where to go from here": [[58, "Where-to-go-from-here"]], "Neural Networks": [[59, "Neural-Networks"]], "The MNIST Data Set": [[59, "The-MNIST-Data-Set"]], "Load the data": [[59, "Load-the-data"]], "Normalize the data": [[59, "Normalize-the-data"]], "Preparing training and testing data": [[59, "Preparing-training-and-testing-data"]], "A Single Neuron": [[59, "A-Single-Neuron"]], "Forward Propogation": [[59, "Forward-Propogation"]], "Loss Function": [[59, "Loss-Function"], [59, "id1"]], "Trainging the Network": [[59, "Trainging-the-Network"]], "Backward Propagation": [[59, "Backward-Propagation"]], "Stochastic Gradient Descent": [[59, "Stochastic-Gradient-Descent"]], "Build an Train": [[59, "Build-an-Train"]], "Testing our model": [[59, "Testing-our-model"]], "Network with Hidden Layers": [[59, "Network-with-Hidden-Layers"]], "Multiclass Network": [[59, "Multiclass-Network"]], "Changes to the model": [[59, "Changes-to-the-model"]], "Forward Pass": [[59, "Forward-Pass"]], "Back Propagation": [[59, "Back-Propagation"]], "Build and Train": [[59, "Build-and-Train"]], "Model performance": [[59, "Model-performance"]], "Test the model": [[59, "Test-the-model"]], "Neural Network with Keras": [[60, "Neural-Network-with-Keras"]], "MNIST Data Set (Keras)": [[60, "MNIST-Data-Set-(Keras)"]], "Build the model": [[60, "Build-the-model"]], "Compile the model": [[60, "Compile-the-model"]], "Train the model": [[60, "Train-the-model"]], "Testing the model": [[60, "Testing-the-model"]], "Convolutional Neural Networks": [[61, "Convolutional-Neural-Networks"]], "Layout of a CNN": [[61, "Layout-of-a-CNN"]], "Convolutional Layer": [[61, "Convolutional-Layer"]], "Padding": [[61, "Padding"]], "Striding": [[61, "Striding"]], "RELU Activation": [[61, "RELU-Activation"]], "Pooling Layer": [[61, "Pooling-Layer"]], "Output Size": [[61, "Output-Size"]], "Flattening": [[61, "Flattening"]], "Dropout": [[61, "Dropout"]], "Fully Connected Layer": [[61, "Fully-Connected-Layer"]], "Example CNN with Keras": [[61, "Example-CNN-with-Keras"]], "Prepare the data": [[61, "Prepare-the-data"]], "Build the network": [[61, "Build-the-network"]], "Train the network": [[61, "Train-the-network"]], "Evaluate the trained network": [[61, "Evaluate-the-trained-network"]], "Evaluate the accuracy of your visual neural network ;-)": [[61, "Evaluate-the-accuracy-of-your-visual-neural-network-;-)"]], "Autoencoder CNN for Time Series Denoising": [[62, "Autoencoder-CNN-for-Time-Series-Denoising"]], "Autoencoder Structure and Purpose": [[62, "Autoencoder-Structure-and-Purpose"]], "Data Generation": [[62, "Data-Generation"]], "Create the Autoencoder network": [[62, "Create-the-Autoencoder-network"]], "Define model data": [[62, "Define-model-data"]], "Encoder/Decoder Setup": [[62, "Encoder/Decoder-Setup"]], "Training the encoder": [[62, "Training-the-encoder"]], "Reconstruction of the Data": [[62, "Reconstruction-of-the-Data"]], "Python and Hardware": [[63, "Python-and-Hardware"]], "Arduino Nano Board": [[63, "Arduino-Nano-Board"]], "Arduino Software": [[63, "Arduino-Software"]], "Setup your board": [[63, "Setup-your-board"]], "Select Firmata Sketch": [[63, "Select-Firmata-Sketch"]], "Communicating with the board": [[63, "Communicating-with-the-board"]], "Let the on-board LED blink": [[63, "Let-the-on-board-LED-blink"]], "Tunable output": [[63, "Tunable-output"]], "Creating an Oscilloscope": [[63, "Creating-an-Oscilloscope"]], "Project: YOUR PROJECT TITLE": [[64, "Project:-YOUR-PROJECT-TITLE"]], "Introduction": [[64, "Introduction"]], "Fundamentals": [[64, "Fundamentals"]], "Results and Discussion": [[64, "Results-and-Discussion"]], "Summary": [[64, "Summary"]], "NumPy arrays": [[65, "NumPy-arrays"]], "Creating Numpy Arrays": [[65, "Creating-Numpy-Arrays"]], "From lists": [[65, "From-lists"]], "Using array-generating functions": [[65, "Using-array-generating-functions"]], "linspace and logspace": [[65, "linspace-and-logspace"]], "mgrid": [[65, "mgrid"]], "diag": [[65, "diag"]], "zeros and ones": [[65, "zeros-and-ones"]], "Manipulating NumPy arrays": [[65, "Manipulating-NumPy-arrays"]], "Slicing": [[65, "Slicing"]], "Reshaping": [[65, "Reshaping"]], "Adding a new dimension: newaxis": [[65, "Adding-a-new-dimension:-newaxis"]], "Stacking and repeating arrays": [[65, "Stacking-and-repeating-arrays"]], "Tile and repeat": [[65, "Tile-and-repeat"]], "Concatenate": [[65, "Concatenate"]], "Hstack and vstack": [[65, "Hstack-and-vstack"]], "Applying mathematical functions": [[65, "Applying-mathematical-functions"]], "Operation involving one array": [[65, "Operation-involving-one-array"]], "Operations involving multiple arrays": [[65, "Operations-involving-multiple-arrays"]], "Add On: Making publication ready figures": [[66, "Add-On:-Making-publication-ready-figures"]], "Creating a plot with a specific bounding box size": [[66, "Creating-a-plot-with-a-specific-bounding-box-size"]], "Creating a plot with a specific axis frame size": [[66, "Creating-a-plot-with-a-specific-axis-frame-size"]], "Choosing fonts": [[66, "Choosing-fonts"]], "Plotting data": [[67, "Plotting-data"]], "Simple Plotting - Implicit Version": [[67, "Simple-Plotting---Implicit-Version"]], "Line Plot": [[67, "Line-Plot"]], "Axis Labels": [[67, "Axis-Labels"]], "Legends": [[67, "Legends"]], "Scatter plot": [[67, "Scatter-plot"]], "Histograms": [[67, "Histograms"]], "Combined plots": [[67, "Combined-plots"]], "Saving figures": [[67, "Saving-figures"]], "Plots with error bars": [[67, "Plots-with-error-bars"]], "Setting plotting limits and excluding data": [[67, "Setting-plotting-limits-and-excluding-data"]], "Masked arrays": [[67, "Masked-arrays"]], "Logarithmic plots": [[67, "Logarithmic-plots"]], "Semi-log plots": [[67, "Semi-log-plots"]], "Log-log plots": [[67, "Log-log-plots"]], "Arranging multiple plots": [[67, "Arranging-multiple-plots"]], "Contour and Density Plots": [[67, "Contour-and-Density-Plots"]], "Simple contour plot": [[67, "Simple-contour-plot"]], "Color contour plot": [[67, "Color-contour-plot"]], "Image plot": [[67, "Image-plot"]], "Additional Plotting - Explicit Version": [[67, "Additional-Plotting---Explicit-Version"]], "Plots with Multiple Spines": [[67, "Plots-with-Multiple-Spines"]], "Insets": [[67, "Insets"]], "Spine axis": [[67, "Spine-axis"]], "Polar plot": [[67, "Polar-plot"]], "Text annotation": [[67, "Text-annotation"]], "3D Plotting": [[67, "3D-Plotting"]], "Projection Scence": [[67, "Projection-Scence"]], "Line Plotting in 3D": [[67, "Line-Plotting-in-3D"]], "Surface Plotting": [[67, "Surface-Plotting"]], "Random numbers": [[68, "Random-numbers"]], "Uniformly distributed random numbers": [[68, "Uniformly-distributed-random-numbers"]], "Normally distributed random numbers": [[68, "Normally-distributed-random-numbers"]], "Exponentially distributed numbers": [[68, "Exponentially-distributed-numbers"]], "Random distribution of integers": [[68, "Random-distribution-of-integers"]], "Problem Set 2": [[69, "Problem-Set-2"]], "Input and output": [[70, "Input-and-output"]], "Keyboard input": [[70, "Keyboard-input"]], "Screen output": [[70, "Screen-output"]], "str.format() Formatting": [[70, "str.format()-Formatting"]], "%-Formatting": [[70, "%-Formatting"]], "f-Strings": [[70, "f-Strings"]], "File input/output": [[70, "File-input/output"]], "File I/O with NumPy": [[70, "File-I/O-with-NumPy"]], "Reading data from a text file": [[70, "Reading-data-from-a-text-file"]], "Writing data to a text file": [[70, "Writing-data-to-a-text-file"]], "File I/O with Pandas": [[70, "File-I/O-with-Pandas"]], "Short intro to Pandas": [[70, "Short-intro-to-Pandas"]], "Reading CSV data with Pandas": [[70, "Reading-CSV-data-with-Pandas"]], "Conditionals: if, elif, and else statements": [[71, "Conditionals:-if,-elif,-and-else-statements"]], "If example": [[71, "If-example"]], "If else example": [[71, "If-else-example"]], "If, elif, else example": [[71, "If,-elif,-else-example"]], "Combining conditions": [[71, "Combining-conditions"]], "For loops": [[71, "For-loops"]], "While loops": [[71, "While-loops"]], "Loops and array operations": [[71, "Loops-and-array-operations"], [74, "Loops-and-array-operations"]], "List comprehensions": [[71, "List-comprehensions"]], "Variables in functions": [[72, "Variables-in-functions"]], "Functions with more than one input or output": [[72, "Functions-with-more-than-one-input-or-output"], [74, "Functions-with-more-than-one-input-or-output"]], "Positional and keyword arguments": [[72, "Positional-and-keyword-arguments"], [74, "Positional-and-keyword-arguments"]], "Functions with variable number of arguments": [[72, "Functions-with-variable-number-of-arguments"]], "Unnamed functions (lambda function)": [[72, "Unnamed-functions-(lambda-function)"]], "Functions as arguments of functions": [[72, "Functions-as-arguments-of-functions"]], "Introduction to Computational Software": [[74, "Introduction-to-Computational-Software"]], "Table of Contents": [[74, "Table-of-Contents"]], "Lecture 3": [[74, "Lecture-3"]], "Conditionals": [[74, "Conditionals"]], "if, elif, and else statements": [[74, "if,-elif,-and-else-statements"]], "Logical Operators": [[74, "Logical-Operators"]], "for loops": [[74, "for-loops"]], "while loops": [[74, "while-loops"]], "List Comprehensions": [[74, "List-Comprehensions"]], "User-defined functions": [[74, "User-defined-functions"]], "Faster Array Processing": [[74, "Faster-Array-Processing"]], "Variable number of arguments": [[74, "Variable-number-of-arguments"]], "Numerical differentiation": [[74, "Numerical-differentiation"]], "More differentiation": [[74, "More-differentiation"]], "Classes and Objects": [[76, "Classes-and-Objects"]], "Definition of Classes": [[76, "Definition-of-Classes"]], "Class Methods": [[76, "Class-Methods"]], "The __init__ method": [[76, "The-__init__-method"]], "The __str__ method": [[76, "The-__str__-method"]], "Class and object variables": [[76, "Class-and-object-variables"]], "Brownian Motion": [[77, "Brownian-Motion"]], "Physics": [[77, "Physics"]], "Class Planning": [[77, "Class-Planning"]], "Simulating": [[77, "Simulating"]], "Plotting the trajectories": [[77, "Plotting-the-trajectories"]], "Characterizing the Brownian motion": [[77, "Characterizing-the-Brownian-motion"]], "Calculate the particle speed": [[77, "Calculate-the-particle-speed"]], "Calculate the particle mean squared displacement": [[77, "Calculate-the-particle-mean-squared-displacement"]], "Animations": [[78, "Animations"]], "Import Modules": [[78, "Import-Modules"]], "Particle class": [[78, "Particle-class"]], "Create a set of particles": [[78, "Create-a-set-of-particles"]], "Canvas and drawing function": [[78, "Canvas-and-drawing-function"]], "Threading for animation": [[78, "Threading-for-animation"]], "Numerical Differentiation": [[79, "Numerical-Differentiation"]], "First order derivative": [[79, "First-order-derivative"]], "Matrix version of the first derivative": [[79, "Matrix-version-of-the-first-derivative"]], "Second order derivative": [[79, "Second-order-derivative"]], "SciPy Module": [[79, "SciPy-Module"]], "Matrix version": [[79, "Matrix-version"]], "Numerical Integration": [[80, "Numerical-Integration"]], "Box method": [[80, "Box-method"]], "Trapezoid method": [[80, "Trapezoid-method"]], "Simpson method": [[80, "Simpson-method"]], "Solving ODEs": [[81, "Solving-ODEs"]], "Implicit Solution - Crank Nicholson": [[81, "Implicit-Solution---Crank-Nicholson"]], "Define Matrices": [[81, "Define-Matrices"]], "Use Initial Conditions": [[81, "Use-Initial-Conditions"]], "Explicit Solution - Numerical Integration": [[81, "Explicit-Solution---Numerical-Integration"]], "Euler Method": [[81, "Euler-Method"]], "Euler Cromer Method": [[81, "Euler-Cromer-Method"]], "Midpoint Method": [[81, "Midpoint-Method"]], "Putting it all together": [[81, "Putting-it-all-together"]], "The definition of the problem": [[81, "The-definition-of-the-problem"]], "Solving the problem": [[81, "Solving-the-problem"], [84, "Solving-the-problem"]], "Solving the Harmonic Oscillator in SciPy": [[81, "Solving-the-Harmonic-Oscillator-in-SciPy"]], "Definition": [[81, "Definition"], [81, "id3"], [83, "Definition"]], "Damped Driven Pendulum in SciPy": [[81, "Damped-Driven-Pendulum-in-SciPy"]], "Utilities": [[82, "Utilities"]], "COVID19": [[83, "COVID19"]], "The Kermack-McKendrick Model": [[83, "The-Kermack-McKendrick-Model"]], "Model Equation": [[83, "Model-Equation"]], "Real COVID19 numbers": [[83, "Real-COVID19-numbers"]], "Total number of cases": [[83, "Total-number-of-cases"]], "Number of Deaths": [[83, "Number-of-Deaths"]], "New cases per day": [[83, "New-cases-per-day"]], "Current cases": [[83, "Current-cases"]], "Coupled Pendula": [[84, "Coupled-Pendula"]], "Description of the problem": [[84, "Description-of-the-problem"]], "Sketch": [[84, "Sketch"]], "Equations of motion": [[84, "Equations-of-motion"], [87, "Equations-of-motion"]], "Setting up the function": [[84, "Setting-up-the-function"]], "Define initial parameters": [[84, "Define-initial-parameters"]], "Solve the equation of motion": [[84, "Solve-the-equation-of-motion"]], "Normal Modes": [[84, "Normal-Modes"]], "In-phase motion": [[84, "In-phase-motion"]], "Out-of-phase motion": [[84, "Out-of-phase-motion"]], "Beat case": [[84, "Beat-case"]], "Computation of energy (here for the beat case)": [[84, "Computation-of-energy-(here-for-the-beat-case)"]], "Potential energy of the pendula": [[84, "Potential-energy-of-the-pendula"]], "Potential energy of the spring": [[84, "Potential-energy-of-the-spring"]], "Kinetic energies": [[84, "Kinetic-energies"]], "Total energy": [[84, "Total-energy"]], "Total energy exchange of the pendula": [[84, "Total-energy-exchange-of-the-pendula"]], "Fourier Analysis": [[85, "Fourier-Analysis"]], "Fourier series": [[85, "Fourier-series"]], "Fourier transform": [[85, "Fourier-transform"]], "Frequency analysis of our coupled pendula": [[85, "Frequency-analysis-of-our-coupled-pendula"]], "Appendix: Fourier Analysis of a damped oscillation": [[86, "Appendix:-Fourier-Analysis-of-a-damped-oscillation"]], "Spring Pendulum": [[87, "Spring-Pendulum"]], "Physical Model": [[87, "Physical-Model"], [88, "Physical-Model"], [89, "Physical-Model"]], "Numerical Solution": [[87, 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diff --git a/docs/_sources/course-info/exam.rst.txt b/docs/_sources/course-info/exam.rst.txt
index 6546056..5aad795 100644
--- a/docs/_sources/course-info/exam.rst.txt
+++ b/docs/_sources/course-info/exam.rst.txt
@@ -31,7 +31,7 @@ Grading: Notebooks will be graded based on:
 - quality of the plots (axis labels, readability of the labels)
 - use of concepts we used for the notebooks (use of markdown, multiple code cells )
 
-The deadline for handing in the project is **September 4, 2024** 
+The deadline for handing in the project is **September 4, 2024, at 1pm sharp! Do not miss the deadline!!!!!!**
 
 Please submit your projects via email to Andrea Kramer,  **firstname.surname@uni-leipzig.de**.
 
diff --git a/docs/course-info/exam.html b/docs/course-info/exam.html
index 80daa68..8f5cede 100644
--- a/docs/course-info/exam.html
+++ b/docs/course-info/exam.html
@@ -237,7 +237,7 @@ <h1>Exam<a class="headerlink" href="#exam" title="Permalink to this heading">#</
 <li><p>quality of the plots (axis labels, readability of the labels)</p></li>
 <li><p>use of concepts we used for the notebooks (use of markdown, multiple code cells )</p></li>
 </ul>
-<p>The deadline for handing in the project is <strong>September 4, 2024</strong></p>
+<p>The deadline for handing in the project is <strong>September 4, 2024, at 1pm sharp! Do not miss the deadline!!!!!!</strong></p>
 <p>Please submit your projects via email to Andrea Kramer,  <strong>firstname.surname&#64;uni-leipzig.de</strong>.</p>
 <p>Since many of you asked for some guiding topics and I as well hope that you do not submit a simulation of planetary motion, here are some topics, though some of them might be for the advanced physicist.</p>
 <section id="mechanics">
diff --git a/docs/searchindex.js b/docs/searchindex.js
index 1041b48..9087e62 100644
--- a/docs/searchindex.js
+++ b/docs/searchindex.js
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defined functions": [[0, "User-defined-functions"]], "Lambda function": [[0, "Lambda-function"]], "Exercise 4 Solution": [[1, "Exercise-4-Solution"]], "Creating a Person Class": [[1, "Creating-a-Person-Class"]], "List of particles": [[1, "List-of-particles"]], "Simulation Canvas": [[1, "Simulation-Canvas"]], "Run the Simulation": [[1, "Run-the-Simulation"]], "Analysis": [[1, "Analysis"]], "Recovery": [[1, "Recovery"]], "For the Experts": [[1, "For-the-Experts"]], "Exercise 5 Solution": [[2, "Exercise-5-Solution"]], "Exercise 7 Solution": [[3, "Exercise-7-Solution"]], "Resolution of an optical Microscope": [[3, "Resolution-of-an-optical-Microscope"]], "Spherical Wave Study": [[3, "Spherical-Wave-Study"]], "Task 1": [[3, "Task-1"]], "Task 2": [[3, "Task-2"]], "Task 3": [[3, "Task-3"]], "Task 4": [[3, "Task-4"]], "Task 5": [[3, "Task-5"]], "Additional task: Resolution and Numerical Aperture": [[3, "Additional-task:-Resolution-and-Numerical-Aperture"]], "Task 6": [[3, "Task-6"]], "Instructor": [[6, "instructor"]], "Course Schedule": [[8, "course-schedule"]], "This Website": [[9, "this-website"]], "Welcome to the Introduction to Computer-based Physical Modeling Course!": [[11, "welcome-to-the-introduction-to-computer-based-physical-modeling-course"], [10, "welcome-to-the-introduction-to-computer-based-physical-modeling-course"]], "Course Information:": [[11, null], [10, null]], "Jupyter Notebooks:": [[11, null], [10, null]], "Lecture 1:": [[11, null], [10, null]], "Lecture 2:": [[11, null]], "Lecture 3:": [[11, null]], "Lecture 4:": [[11, null]], "Lecture 5:": [[11, null]], "Lecture 6:": [[11, null]], "Lecture 7:": [[11, null]], "Lecture 8:": [[11, null]], "Lecture 9:": [[11, null]], "Lecture 10:": [[11, null]], "Lecture 11:": [[11, null]], "Lecture 12:": [[11, null]], "Lecture 13:": [[11, null]], "Lecture 14:": [[11, null]], "Lecture 15:": [[11, null]], "Indices and tables": [[11, "indices-and-tables"], [10, "indices-and-tables"]], "Overview": [[12, "overview"], [58, "Overview"]], "Lecture Contents": [[14, "lecture-contents"], [15, "lecture-contents"], [16, "lecture-contents"], [17, "lecture-contents"], [18, "lecture-contents"], [19, "lecture-contents"], [20, "lecture-contents"], [23, "lecture-contents"], [25, "lecture-contents"], [27, "lecture-contents"], [28, "lecture-contents"], [30, "lecture-contents"], [32, "lecture-contents"], [34, "lecture-contents"], [35, "lecture-contents"], [37, "lecture-contents"]], "Creating a figure, which just looks nice on the screen": [[21, "Creating-a-figure,-which-just-looks-nice-on-the-screen"]], "Creating a figure, which looks good in paper and on screen": [[21, "Creating-a-figure,-which-looks-good-in-paper-and-on-screen"]], "Exercise 2": [[22, "exercise-2"]], "Exercise 3": [[24, "exercise-3"]], "Exercise 4": [[26, "exercise-4"]], "Exercise 5": [[29, "exercise-5"]], "Exercise 6": [[33, "exercise-6"]], "Exercise 7": [[36, "exercise-7"], [31, "exercise-7"]], "Entering code": [[40, "Entering-code"]], "Entering Markdown": [[40, "Entering-Markdown"]], "Markdown basics": [[40, "Markdown-basics"]], "Headings": [[40, "Headings"]], "Embedded code": [[40, "Embedded-code"]], "LaTeX equations": [[40, "LaTeX-equations"]], "Images": [[40, "Images"]], "Videos": [[40, "Videos"]], "An empty notebook": [[41, "An-empty-notebook"]], "Variables and types": [[43, "Variables-and-types"], [47, "Variables-and-types"]], "Symbol names": [[43, "Symbol-names"], [47, "Symbol-names"]], "Variable Assignment": [[43, "Variable-Assignment"], [47, "Variable-Assignment"]], "Number types": [[43, "Number-types"], [47, "Number-types"]], "Integers": [[43, "Integers"], [47, "Integers"]], "Floating Point": [[43, "Floating-Point"], [47, "Floating-Point"]], "Complex Numbers": [[43, "Complex-Numbers"], [47, "Complex-Numbers"]], "Type conversion": [[43, "Type-conversion"]], "Operators and comparisons": [[44, "Operators-and-comparisons"], [47, "Operators-and-comparisons"]], "Data Types in Python": [[45, "Data-Types-in-Python"], [47, "Data-Types-in-Python"]], "Strings": [[45, "Strings"], [47, "Strings"]], "Lists": [[45, "Lists"], [47, "Lists"]], "Tuples": [[45, "Tuples"], [47, "Tuples"]], "Dictionaries": [[45, "Dictionaries"], [47, "Dictionaries"]], "Sets": [[45, "Sets"]], "Modules and namespaces": [[46, "Modules-and-namespaces"]], "Modules": [[46, "Modules"], [47, "Modules"]], "Namespaces": [[46, "Namespaces"]], "Contents of a module": [[46, "Contents-of-a-module"]], "Type casting": [[47, "Type-casting"]], "Contents and documentation of a module": [[47, "Contents-and-documentation-of-a-module"]], "Exceptions": [[47, "Exceptions"], [48, "Exceptions"], [73, "Exceptions"]], "What\u2019s next": [[47, "What's-next"]], "Quantum Mechanics": [[49, "Quantum-Mechanics"], [5, "quantum-mechanics"]], "Quantum Mechanics in a Nutshell": [[49, "Quantum-Mechanics-in-a-Nutshell"]], "Time dependent Schr\u00f6dinger equation": [[49, "Time-dependent-Schr\u00f6dinger-equation"], [53, "Time-dependent-Schr\u00f6dinger-equation"]], "Stationary Schr\u00f6dinger equation": [[49, "Stationary-Schr\u00f6dinger-equation"]], "Recap: Implicit Solution": [[49, "Recap:-Implicit-Solution"]], "Kinetic energy": [[49, "Kinetic-energy"], [50, "Kinetic-energy"], [51, "Kinetic-energy"], [52, "Kinetic-energy"]], "Potential energy": [[49, "Potential-energy"], [50, "Potential-energy"], [51, "Potential-energy"], [52, "Potential-energy"]], "Particle in a box": [[50, "Particle-in-a-box"]], "Definition of the problem": [[50, "Definition-of-the-problem"], [51, "Definition-of-the-problem"], [52, "Definition-of-the-problem"]], "Solution": [[50, "Solution"], [51, "Solution"], [52, "Solution"], [81, "Solution"], [81, "id1"], [81, "id4"], [83, "Solution"], [87, "Solution"], [89, "Solution"]], "Plotting": [[50, "Plotting"], [51, "Plotting"], [52, "Plotting"], [81, "Plotting"], [81, "id5"], [83, "Plotting"], [84, "Plotting"], [87, "Plotting"]], "Energies of bound states": [[50, "Energies-of-bound-states"]], "Where to go from here?": [[50, "Where-to-go-from-here?"], [51, "Where-to-go-from-here?"], [52, "Where-to-go-from-here?"], [54, "Where-to-go-from-here?"], [55, "Where-to-go-from-here?"], [61, "Where-to-go-from-here?"]], "Harmonic Oscillator": [[51, "Harmonic-Oscillator"], [81, "Harmonic-Oscillator"]], "Energies of the states": [[51, "Energies-of-the-states"]], "Periodic Potential": [[52, "Periodic-Potential"]], "Energy states": [[52, "Energy-states"]], "Time Dependent Quantum Mechanics": [[53, "Time-Dependent-Quantum-Mechanics"]], "Wavepackets": [[53, "Wavepackets"]], "Demonstration of superposition of plane waves": [[53, "Demonstration-of-superposition-of-plane-waves"]], "Wavepacket": [[53, "Wavepacket"]], "Wavepacket with rectangular amplitude": [[53, "Wavepacket-with-rectangular-amplitude"]], "Gaussian Wave Packet": [[53, "Gaussian-Wave-Packet"]], "Time evolution of a Gaussian Wavepacket": [[53, "Time-evolution-of-a-Gaussian-Wavepacket"]], "Wavepacket in a Potential Box": [[54, "Wavepacket-in-a-Potential-Box"]], "Problem Setup": [[54, "Problem-Setup"]], "Initial conditions": [[54, "Initial-conditions"]], "Eigenfunctions": [[54, "Eigenfunctions"]], "Quality of the coefficients": [[54, "Quality-of-the-coefficients"]], "Animation": [[54, "Animation"], [55, "Animation"], [55, "id3"], [84, "Animation"], [92, "Animation"], [93, "Animation"], [95, "Animation"]], "Tunneling through a barrier": [[55, "Tunneling-through-a-barrier"]], "Schr\u00f6dinger equation for the momentum": [[55, "Schr\u00f6dinger-equation-for-the-momentum"]], "Crank Nicolson Solution": [[55, "Crank-Nicolson-Solution"]], "Setup Domain": [[55, "Setup-Domain"], [55, "id1"], [89, "Setup-Domain"]], "Initial Conditions": [[55, "Initial-Conditions"], [57, "Initial-Conditions"], [89, "Initial-Conditions"]], "Matrix Setup": [[55, "Matrix-Setup"], [89, "Matrix-Setup"]], "Propagation Matrix": [[55, "Propagation-Matrix"]], "Animation setup": [[55, "Animation-setup"], [55, "id2"]], "Split Step Method": [[55, "Split-Step-Method"], [56, "Split-Step-Method"]], "Potential energy landscape": [[55, "Potential-energy-landscape"]], "Initial wavepacket": [[55, "Initial-wavepacket"]], "Fourier Transform Setup": [[55, "Fourier-Transform-Setup"]], "Phase Factor per Timestep": [[55, "Phase-Factor-per-Timestep"]], "Old Split Step Method": [[56, "Old-Split-Step-Method"]], "Setup the simulation": [[56, "Setup-the-simulation"]], "Hydrodynamics": [[57, "Hydrodynamics"]], "Falling sphere": [[57, "Falling-sphere"]], "Setup": [[57, "Setup"], [81, "Setup"], [81, "id2"], [83, "Setup"]], "Function definition": [[57, "Function-definition"], [72, "Function-definition"]], "Numerical solution": [[57, "Numerical-solution"]], "Analytical solution": [[57, "Analytical-solution"]], "Stokes equation": [[57, "Stokes-equation"]], "Fundamental Solutions of the Stokes Equation": [[57, "Fundamental-Solutions-of-the-Stokes-Equation"]], "Stokeslet": [[57, "Stokeslet"]], "Source dipole": [[57, "Source-dipole"]], "Sum of both solutions": [[57, "Sum-of-both-solutions"]], "Machine Learning and Neural Networks": [[58, "Machine-Learning-and-Neural-Networks"]], "Reinforcement Learning": [[58, "Reinforcement-Learning"]], "Markov Decision Process": [[58, "Markov-Decision-Process"]], "Methods or RL": [[58, "Methods-or-RL"]], "Navigating a Grid World": [[58, "Navigating-a-Grid-World"]], "Initialize Reinforcement Learning": [[58, "Initialize-Reinforcement-Learning"]], "List of actions": [[58, "List-of-actions"]], "Initial state": [[58, "Initial-state"]], "Reinforcement Learning Loop": [[58, "Reinforcement-Learning-Loop"]], "Convergence of the Q-learning": [[58, "Convergence-of-the-Q-learning"]], "Policy": [[58, "Policy"]], "Plot the policy": [[58, "Plot-the-policy"]], "Where to go from here": [[58, "Where-to-go-from-here"]], "Neural Networks": [[59, "Neural-Networks"]], "The MNIST Data Set": [[59, "The-MNIST-Data-Set"]], "Load the data": [[59, "Load-the-data"]], "Normalize the data": [[59, "Normalize-the-data"]], "Preparing training and testing data": [[59, "Preparing-training-and-testing-data"]], "A Single Neuron": [[59, "A-Single-Neuron"]], "Forward Propogation": [[59, "Forward-Propogation"]], "Loss Function": [[59, "Loss-Function"], [59, "id1"]], "Trainging the Network": [[59, "Trainging-the-Network"]], "Backward Propagation": [[59, "Backward-Propagation"]], "Stochastic Gradient Descent": [[59, "Stochastic-Gradient-Descent"]], "Build an Train": [[59, "Build-an-Train"]], "Testing our model": [[59, "Testing-our-model"]], "Network with Hidden Layers": [[59, "Network-with-Hidden-Layers"]], "Multiclass Network": [[59, "Multiclass-Network"]], "Changes to the model": [[59, "Changes-to-the-model"]], "Forward Pass": [[59, "Forward-Pass"]], "Back Propagation": [[59, "Back-Propagation"]], "Build and Train": [[59, "Build-and-Train"]], "Model performance": [[59, "Model-performance"]], "Test the model": [[59, "Test-the-model"]], "Neural Network with Keras": [[60, "Neural-Network-with-Keras"]], "MNIST Data Set (Keras)": [[60, "MNIST-Data-Set-(Keras)"]], "Build the model": [[60, "Build-the-model"]], "Compile the model": [[60, "Compile-the-model"]], "Train the model": [[60, "Train-the-model"]], "Testing the model": [[60, "Testing-the-model"]], "Convolutional Neural Networks": [[61, "Convolutional-Neural-Networks"]], "Layout of a CNN": [[61, "Layout-of-a-CNN"]], "Convolutional Layer": [[61, "Convolutional-Layer"]], "Padding": [[61, "Padding"]], "Striding": [[61, "Striding"]], "RELU Activation": [[61, "RELU-Activation"]], "Pooling Layer": [[61, "Pooling-Layer"]], "Output Size": [[61, "Output-Size"]], "Flattening": [[61, "Flattening"]], "Dropout": [[61, "Dropout"]], "Fully Connected Layer": [[61, "Fully-Connected-Layer"]], "Example CNN with Keras": [[61, "Example-CNN-with-Keras"]], "Prepare the data": [[61, "Prepare-the-data"]], "Build the network": [[61, "Build-the-network"]], "Train the network": [[61, "Train-the-network"]], "Evaluate the trained network": [[61, "Evaluate-the-trained-network"]], "Evaluate the accuracy of your visual neural network ;-)": [[61, "Evaluate-the-accuracy-of-your-visual-neural-network-;-)"]], "Autoencoder CNN for Time Series Denoising": [[62, "Autoencoder-CNN-for-Time-Series-Denoising"]], "Autoencoder Structure and Purpose": [[62, "Autoencoder-Structure-and-Purpose"]], "Data Generation": [[62, "Data-Generation"]], "Create the Autoencoder network": [[62, "Create-the-Autoencoder-network"]], "Define model data": [[62, "Define-model-data"]], "Encoder/Decoder Setup": [[62, "Encoder/Decoder-Setup"]], "Training the encoder": [[62, "Training-the-encoder"]], "Reconstruction of the Data": [[62, "Reconstruction-of-the-Data"]], "Python and Hardware": [[63, "Python-and-Hardware"]], "Arduino Nano Board": [[63, "Arduino-Nano-Board"]], "Arduino Software": [[63, "Arduino-Software"]], "Setup your board": [[63, "Setup-your-board"]], "Select Firmata Sketch": [[63, "Select-Firmata-Sketch"]], "Communicating with the board": [[63, "Communicating-with-the-board"]], "Let the on-board LED blink": [[63, "Let-the-on-board-LED-blink"]], "Tunable output": [[63, "Tunable-output"]], "Creating an Oscilloscope": [[63, "Creating-an-Oscilloscope"]], "Project: YOUR PROJECT TITLE": [[64, "Project:-YOUR-PROJECT-TITLE"]], "Introduction": [[64, "Introduction"]], "Fundamentals": [[64, "Fundamentals"]], "Results and Discussion": [[64, "Results-and-Discussion"]], "Summary": [[64, "Summary"]], "NumPy arrays": [[65, "NumPy-arrays"]], "Creating Numpy Arrays": [[65, "Creating-Numpy-Arrays"]], "From lists": [[65, "From-lists"]], "Using array-generating functions": [[65, "Using-array-generating-functions"]], "linspace and logspace": [[65, "linspace-and-logspace"]], "mgrid": [[65, "mgrid"]], "diag": [[65, "diag"]], "zeros and ones": [[65, "zeros-and-ones"]], "Manipulating NumPy arrays": [[65, "Manipulating-NumPy-arrays"]], "Slicing": [[65, "Slicing"]], "Reshaping": [[65, "Reshaping"]], "Adding a new dimension: newaxis": [[65, "Adding-a-new-dimension:-newaxis"]], "Stacking and repeating arrays": [[65, "Stacking-and-repeating-arrays"]], "Tile and repeat": [[65, "Tile-and-repeat"]], "Concatenate": [[65, "Concatenate"]], "Hstack and vstack": [[65, "Hstack-and-vstack"]], "Applying mathematical functions": [[65, "Applying-mathematical-functions"]], "Operation involving one array": [[65, "Operation-involving-one-array"]], "Operations involving multiple arrays": [[65, "Operations-involving-multiple-arrays"]], "Add On: Making publication ready figures": [[66, "Add-On:-Making-publication-ready-figures"]], "Creating a plot with a specific bounding box size": [[66, "Creating-a-plot-with-a-specific-bounding-box-size"]], "Creating a plot with a specific axis frame size": [[66, "Creating-a-plot-with-a-specific-axis-frame-size"]], "Choosing fonts": [[66, "Choosing-fonts"]], "Plotting data": [[67, "Plotting-data"]], "Simple Plotting - Implicit Version": [[67, "Simple-Plotting---Implicit-Version"]], "Line Plot": [[67, "Line-Plot"]], "Axis Labels": [[67, "Axis-Labels"]], "Legends": [[67, "Legends"]], "Scatter plot": [[67, "Scatter-plot"]], "Histograms": [[67, "Histograms"]], "Combined plots": [[67, "Combined-plots"]], "Saving figures": [[67, "Saving-figures"]], "Plots with error bars": [[67, "Plots-with-error-bars"]], "Setting plotting limits and excluding data": [[67, "Setting-plotting-limits-and-excluding-data"]], "Masked arrays": [[67, "Masked-arrays"]], "Logarithmic plots": [[67, "Logarithmic-plots"]], "Semi-log plots": [[67, "Semi-log-plots"]], "Log-log plots": [[67, "Log-log-plots"]], "Arranging multiple plots": [[67, "Arranging-multiple-plots"]], "Contour and Density Plots": [[67, "Contour-and-Density-Plots"]], "Simple contour plot": [[67, "Simple-contour-plot"]], "Color contour plot": [[67, "Color-contour-plot"]], "Image plot": [[67, "Image-plot"]], "Additional Plotting - Explicit Version": [[67, "Additional-Plotting---Explicit-Version"]], "Plots with Multiple Spines": [[67, "Plots-with-Multiple-Spines"]], "Insets": [[67, "Insets"]], "Spine axis": [[67, "Spine-axis"]], "Polar plot": [[67, "Polar-plot"]], "Text annotation": [[67, "Text-annotation"]], "3D Plotting": [[67, "3D-Plotting"]], "Projection Scence": [[67, "Projection-Scence"]], "Line Plotting in 3D": [[67, "Line-Plotting-in-3D"]], "Surface Plotting": [[67, "Surface-Plotting"]], "Random numbers": [[68, "Random-numbers"]], "Uniformly distributed random numbers": [[68, "Uniformly-distributed-random-numbers"]], "Normally distributed random numbers": [[68, "Normally-distributed-random-numbers"]], "Exponentially distributed numbers": [[68, "Exponentially-distributed-numbers"]], "Random distribution of integers": [[68, "Random-distribution-of-integers"]], "Problem Set 2": [[69, "Problem-Set-2"]], "Input and output": [[70, "Input-and-output"]], "Keyboard input": [[70, "Keyboard-input"]], "Screen output": [[70, "Screen-output"]], "str.format() Formatting": [[70, "str.format()-Formatting"]], "%-Formatting": [[70, "%-Formatting"]], "f-Strings": [[70, "f-Strings"]], "File input/output": [[70, "File-input/output"]], "File I/O with NumPy": [[70, "File-I/O-with-NumPy"]], "Reading data from a text file": [[70, "Reading-data-from-a-text-file"]], "Writing data to a text file": [[70, "Writing-data-to-a-text-file"]], "File I/O with Pandas": [[70, "File-I/O-with-Pandas"]], "Short intro to Pandas": [[70, "Short-intro-to-Pandas"]], "Reading CSV data with Pandas": [[70, "Reading-CSV-data-with-Pandas"]], "Conditionals: if, elif, and else statements": [[71, "Conditionals:-if,-elif,-and-else-statements"]], "If example": [[71, "If-example"]], "If else example": [[71, "If-else-example"]], "If, elif, else example": [[71, "If,-elif,-else-example"]], "Combining conditions": [[71, "Combining-conditions"]], "For loops": [[71, "For-loops"]], "While loops": [[71, "While-loops"]], "Loops and array operations": [[71, "Loops-and-array-operations"], [74, "Loops-and-array-operations"]], "List comprehensions": [[71, "List-comprehensions"]], "Variables in functions": [[72, "Variables-in-functions"]], "Functions with more than one input or output": [[72, "Functions-with-more-than-one-input-or-output"], [74, "Functions-with-more-than-one-input-or-output"]], "Positional and keyword arguments": [[72, "Positional-and-keyword-arguments"], [74, "Positional-and-keyword-arguments"]], "Functions with variable number of arguments": [[72, "Functions-with-variable-number-of-arguments"]], "Unnamed functions (lambda function)": [[72, "Unnamed-functions-(lambda-function)"]], "Functions as arguments of functions": [[72, "Functions-as-arguments-of-functions"]], "Introduction to Computational Software": [[74, "Introduction-to-Computational-Software"]], "Table of Contents": [[74, "Table-of-Contents"]], "Lecture 3": [[74, "Lecture-3"]], "Conditionals": [[74, "Conditionals"]], "if, elif, and else statements": [[74, "if,-elif,-and-else-statements"]], "Logical Operators": [[74, "Logical-Operators"]], "for loops": [[74, "for-loops"]], "while loops": [[74, "while-loops"]], "List Comprehensions": [[74, "List-Comprehensions"]], "User-defined functions": [[74, "User-defined-functions"]], "Faster Array Processing": [[74, "Faster-Array-Processing"]], "Variable number of arguments": [[74, "Variable-number-of-arguments"]], "Numerical differentiation": [[74, "Numerical-differentiation"]], "More differentiation": [[74, "More-differentiation"]], "Classes and Objects": [[76, "Classes-and-Objects"]], "Definition of Classes": [[76, "Definition-of-Classes"]], "Class Methods": [[76, "Class-Methods"]], "The __init__ method": [[76, "The-__init__-method"]], "The __str__ method": [[76, "The-__str__-method"]], "Class and object variables": [[76, "Class-and-object-variables"]], "Brownian Motion": [[77, "Brownian-Motion"]], "Physics": [[77, "Physics"]], "Class Planning": [[77, "Class-Planning"]], "Simulating": [[77, "Simulating"]], "Plotting the trajectories": [[77, "Plotting-the-trajectories"]], "Characterizing the 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"Functions"]], "User defined functions": [[0, "User-defined-functions"]], "Lambda function": [[0, "Lambda-function"]], "Exercise 4 Solution": [[1, "Exercise-4-Solution"]], "Creating a Person Class": [[1, "Creating-a-Person-Class"]], "List of particles": [[1, "List-of-particles"]], "Simulation Canvas": [[1, "Simulation-Canvas"]], "Run the Simulation": [[1, "Run-the-Simulation"]], "Analysis": [[1, "Analysis"]], "Recovery": [[1, "Recovery"]], "For the Experts": [[1, "For-the-Experts"]], "Exercise 5 Solution": [[2, "Exercise-5-Solution"]], "Exercise 7 Solution": [[3, "Exercise-7-Solution"]], "Resolution of an optical Microscope": [[3, "Resolution-of-an-optical-Microscope"]], "Spherical Wave Study": [[3, "Spherical-Wave-Study"]], "Task 1": [[3, "Task-1"]], "Task 2": [[3, "Task-2"]], "Task 3": [[3, "Task-3"]], "Task 4": [[3, "Task-4"]], "Task 5": [[3, "Task-5"]], "Additional task: Resolution and Numerical Aperture": [[3, "Additional-task:-Resolution-and-Numerical-Aperture"]], "Task 6": [[3, "Task-6"]], "Instructor": [[6, "instructor"]], "This Website": [[9, "this-website"]], "Welcome to the Introduction to Computer-based Physical Modeling Course!": [[11, "welcome-to-the-introduction-to-computer-based-physical-modeling-course"], [10, "welcome-to-the-introduction-to-computer-based-physical-modeling-course"]], "Course Information:": [[11, null], [10, null]], "Jupyter Notebooks:": [[11, null], [10, null]], "Lecture 1:": [[11, null], [10, null]], "Lecture 2:": [[11, null]], "Lecture 3:": [[11, null]], "Lecture 4:": [[11, null]], "Lecture 5:": [[11, null]], "Lecture 6:": [[11, null]], "Lecture 7:": [[11, null]], "Lecture 8:": [[11, null]], "Lecture 9:": [[11, null]], "Lecture 10:": [[11, null]], "Lecture 11:": [[11, null]], "Lecture 12:": [[11, null]], "Lecture 13:": [[11, null]], "Lecture 14:": [[11, null]], "Lecture 15:": [[11, null]], "Indices and tables": [[11, "indices-and-tables"], [10, "indices-and-tables"]], "Overview": [[12, "overview"], [58, "Overview"]], "Lecture Contents": [[14, "lecture-contents"], [15, "lecture-contents"], [16, "lecture-contents"], [17, "lecture-contents"], [18, "lecture-contents"], [19, "lecture-contents"], [20, "lecture-contents"], [23, "lecture-contents"], [25, "lecture-contents"], [27, "lecture-contents"], [28, "lecture-contents"], [30, "lecture-contents"], [32, "lecture-contents"], [34, "lecture-contents"], [35, "lecture-contents"], [37, "lecture-contents"]], "Creating a figure, which just looks nice on the screen": [[21, "Creating-a-figure,-which-just-looks-nice-on-the-screen"]], "Creating a figure, which looks good in paper and on screen": [[21, "Creating-a-figure,-which-looks-good-in-paper-and-on-screen"]], "Exercise 2": [[22, "exercise-2"]], "Exercise 3": [[24, "exercise-3"]], "Exercise 4": [[26, "exercise-4"]], "Exercise 5": [[29, "exercise-5"]], "Exercise 6": [[33, "exercise-6"]], "Exercise 7": [[36, "exercise-7"], [31, "exercise-7"]], "Entering code": [[40, "Entering-code"]], "Entering Markdown": [[40, "Entering-Markdown"]], "Markdown basics": [[40, "Markdown-basics"]], "Headings": [[40, "Headings"]], "Embedded code": [[40, "Embedded-code"]], "LaTeX equations": [[40, "LaTeX-equations"]], "Images": [[40, "Images"]], "Videos": [[40, "Videos"]], "An empty notebook": [[41, "An-empty-notebook"]], "Variables and types": [[43, "Variables-and-types"], [47, "Variables-and-types"]], "Symbol names": [[43, "Symbol-names"], [47, "Symbol-names"]], "Variable Assignment": [[43, "Variable-Assignment"], [47, "Variable-Assignment"]], "Number types": [[43, "Number-types"], [47, "Number-types"]], "Integers": [[43, "Integers"], [47, "Integers"]], "Floating Point": [[43, "Floating-Point"], [47, "Floating-Point"]], "Complex Numbers": [[43, "Complex-Numbers"], [47, "Complex-Numbers"]], "Type conversion": [[43, "Type-conversion"]], "Operators and comparisons": [[44, "Operators-and-comparisons"], [47, "Operators-and-comparisons"]], "Data Types in Python": [[45, "Data-Types-in-Python"], [47, "Data-Types-in-Python"]], "Strings": [[45, "Strings"], [47, "Strings"]], "Lists": [[45, "Lists"], [47, "Lists"]], "Tuples": [[45, "Tuples"], [47, "Tuples"]], "Dictionaries": [[45, "Dictionaries"], [47, "Dictionaries"]], "Sets": [[45, "Sets"]], "Modules and namespaces": [[46, "Modules-and-namespaces"]], "Modules": [[46, "Modules"], [47, "Modules"]], "Namespaces": [[46, "Namespaces"]], "Contents of a module": [[46, "Contents-of-a-module"]], "Type casting": [[47, "Type-casting"]], "Contents and documentation of a module": [[47, "Contents-and-documentation-of-a-module"]], "Exceptions": [[47, "Exceptions"], [48, "Exceptions"], [73, "Exceptions"]], "What\u2019s next": [[47, "What's-next"]], "Quantum Mechanics": [[49, "Quantum-Mechanics"], [5, "quantum-mechanics"]], "Quantum Mechanics in a Nutshell": [[49, "Quantum-Mechanics-in-a-Nutshell"]], "Time dependent Schr\u00f6dinger equation": [[49, "Time-dependent-Schr\u00f6dinger-equation"], [53, "Time-dependent-Schr\u00f6dinger-equation"]], "Stationary Schr\u00f6dinger equation": [[49, "Stationary-Schr\u00f6dinger-equation"]], "Recap: Implicit Solution": [[49, "Recap:-Implicit-Solution"]], "Kinetic energy": [[49, "Kinetic-energy"], [50, "Kinetic-energy"], [51, "Kinetic-energy"], [52, "Kinetic-energy"]], "Potential energy": [[49, "Potential-energy"], [50, "Potential-energy"], [51, "Potential-energy"], [52, "Potential-energy"]], "Particle in a box": [[50, "Particle-in-a-box"]], "Definition of the problem": [[50, "Definition-of-the-problem"], [51, "Definition-of-the-problem"], [52, "Definition-of-the-problem"]], "Solution": [[50, "Solution"], [51, "Solution"], [52, "Solution"], [81, "Solution"], [81, "id1"], [81, "id4"], [83, "Solution"], [87, "Solution"], [89, "Solution"]], "Plotting": [[50, "Plotting"], [51, "Plotting"], [52, "Plotting"], [81, "Plotting"], [81, "id5"], [83, "Plotting"], [84, "Plotting"], [87, "Plotting"]], "Energies of bound states": [[50, "Energies-of-bound-states"]], "Where to go from here?": [[50, "Where-to-go-from-here?"], [51, "Where-to-go-from-here?"], [52, "Where-to-go-from-here?"], [54, "Where-to-go-from-here?"], [55, "Where-to-go-from-here?"], [61, "Where-to-go-from-here?"]], "Harmonic Oscillator": [[51, "Harmonic-Oscillator"], [81, "Harmonic-Oscillator"]], "Energies of the states": [[51, "Energies-of-the-states"]], "Periodic Potential": [[52, "Periodic-Potential"]], "Energy states": [[52, "Energy-states"]], "Time Dependent Quantum Mechanics": [[53, "Time-Dependent-Quantum-Mechanics"]], "Wavepackets": [[53, "Wavepackets"]], "Demonstration of superposition of plane waves": [[53, "Demonstration-of-superposition-of-plane-waves"]], "Wavepacket": [[53, "Wavepacket"]], "Wavepacket with rectangular amplitude": [[53, "Wavepacket-with-rectangular-amplitude"]], "Gaussian Wave Packet": [[53, "Gaussian-Wave-Packet"]], "Time evolution of a Gaussian Wavepacket": [[53, "Time-evolution-of-a-Gaussian-Wavepacket"]], "Wavepacket in a Potential Box": [[54, "Wavepacket-in-a-Potential-Box"]], "Problem Setup": [[54, "Problem-Setup"]], "Initial conditions": [[54, "Initial-conditions"]], "Eigenfunctions": [[54, "Eigenfunctions"]], "Quality of the coefficients": [[54, "Quality-of-the-coefficients"]], "Animation": [[54, "Animation"], [55, "Animation"], [55, "id3"], [84, "Animation"], [92, "Animation"], [93, "Animation"], [95, "Animation"]], "Tunneling through a barrier": [[55, "Tunneling-through-a-barrier"]], "Schr\u00f6dinger equation for the momentum": [[55, "Schr\u00f6dinger-equation-for-the-momentum"]], "Crank Nicolson Solution": [[55, "Crank-Nicolson-Solution"]], "Setup Domain": [[55, "Setup-Domain"], [55, "id1"], [89, "Setup-Domain"]], "Initial Conditions": [[55, "Initial-Conditions"], [57, "Initial-Conditions"], [89, "Initial-Conditions"]], "Matrix Setup": [[55, "Matrix-Setup"], [89, "Matrix-Setup"]], "Propagation Matrix": [[55, "Propagation-Matrix"]], "Animation setup": [[55, "Animation-setup"], [55, "id2"]], "Split Step Method": [[55, "Split-Step-Method"], [56, "Split-Step-Method"]], "Potential energy landscape": [[55, "Potential-energy-landscape"]], "Initial wavepacket": [[55, "Initial-wavepacket"]], "Fourier Transform Setup": [[55, "Fourier-Transform-Setup"]], "Phase Factor per Timestep": [[55, "Phase-Factor-per-Timestep"]], "Old Split Step Method": [[56, "Old-Split-Step-Method"]], "Setup the simulation": [[56, "Setup-the-simulation"]], "Hydrodynamics": [[57, "Hydrodynamics"]], "Falling sphere": [[57, "Falling-sphere"]], "Setup": [[57, "Setup"], [81, "Setup"], [81, "id2"], [83, "Setup"]], "Function definition": [[57, "Function-definition"], [72, "Function-definition"]], "Numerical solution": [[57, "Numerical-solution"]], "Analytical solution": [[57, "Analytical-solution"]], "Stokes equation": [[57, "Stokes-equation"]], "Fundamental Solutions of the Stokes Equation": [[57, "Fundamental-Solutions-of-the-Stokes-Equation"]], "Stokeslet": [[57, "Stokeslet"]], "Source dipole": [[57, "Source-dipole"]], "Sum of both solutions": [[57, "Sum-of-both-solutions"]], "Machine Learning and Neural Networks": [[58, "Machine-Learning-and-Neural-Networks"]], "Reinforcement Learning": [[58, "Reinforcement-Learning"]], "Markov Decision Process": [[58, "Markov-Decision-Process"]], "Methods or RL": [[58, "Methods-or-RL"]], "Navigating a Grid World": [[58, "Navigating-a-Grid-World"]], "Initialize Reinforcement Learning": [[58, "Initialize-Reinforcement-Learning"]], "List of actions": [[58, "List-of-actions"]], "Initial state": [[58, "Initial-state"]], "Reinforcement Learning Loop": [[58, "Reinforcement-Learning-Loop"]], "Convergence of the Q-learning": [[58, "Convergence-of-the-Q-learning"]], "Policy": [[58, "Policy"]], "Plot the policy": [[58, "Plot-the-policy"]], "Where to go from here": [[58, "Where-to-go-from-here"]], "Neural Networks": [[59, "Neural-Networks"]], "The MNIST Data Set": [[59, "The-MNIST-Data-Set"]], "Load the data": [[59, "Load-the-data"]], "Normalize the data": [[59, "Normalize-the-data"]], "Preparing training and testing data": [[59, "Preparing-training-and-testing-data"]], "A Single Neuron": [[59, "A-Single-Neuron"]], "Forward Propogation": [[59, "Forward-Propogation"]], "Loss Function": [[59, "Loss-Function"], [59, "id1"]], "Trainging the Network": [[59, "Trainging-the-Network"]], "Backward Propagation": [[59, "Backward-Propagation"]], "Stochastic Gradient Descent": [[59, "Stochastic-Gradient-Descent"]], "Build an Train": [[59, "Build-an-Train"]], "Testing our model": [[59, "Testing-our-model"]], "Network with Hidden Layers": [[59, "Network-with-Hidden-Layers"]], "Multiclass Network": [[59, "Multiclass-Network"]], "Changes to the model": [[59, "Changes-to-the-model"]], "Forward Pass": [[59, "Forward-Pass"]], "Back Propagation": [[59, "Back-Propagation"]], "Build and Train": [[59, "Build-and-Train"]], "Model performance": [[59, "Model-performance"]], "Test the model": [[59, "Test-the-model"]], "Neural Network with Keras": [[60, "Neural-Network-with-Keras"]], "MNIST Data Set (Keras)": [[60, "MNIST-Data-Set-(Keras)"]], "Build the model": [[60, "Build-the-model"]], "Compile the model": [[60, "Compile-the-model"]], "Train the model": [[60, "Train-the-model"]], "Testing the model": [[60, "Testing-the-model"]], "Convolutional Neural Networks": [[61, "Convolutional-Neural-Networks"]], "Layout of a CNN": [[61, "Layout-of-a-CNN"]], "Convolutional Layer": [[61, "Convolutional-Layer"]], "Padding": [[61, "Padding"]], "Striding": [[61, "Striding"]], "RELU Activation": [[61, "RELU-Activation"]], "Pooling Layer": [[61, "Pooling-Layer"]], "Output Size": [[61, "Output-Size"]], "Flattening": [[61, "Flattening"]], "Dropout": [[61, "Dropout"]], "Fully Connected Layer": [[61, "Fully-Connected-Layer"]], "Example CNN with Keras": [[61, "Example-CNN-with-Keras"]], "Prepare the data": [[61, "Prepare-the-data"]], "Build the network": [[61, "Build-the-network"]], "Train the network": [[61, "Train-the-network"]], "Evaluate the trained network": [[61, "Evaluate-the-trained-network"]], "Evaluate the accuracy of your visual neural network ;-)": [[61, "Evaluate-the-accuracy-of-your-visual-neural-network-;-)"]], "Autoencoder CNN for Time Series Denoising": [[62, "Autoencoder-CNN-for-Time-Series-Denoising"]], "Autoencoder Structure and Purpose": [[62, "Autoencoder-Structure-and-Purpose"]], "Data Generation": [[62, "Data-Generation"]], "Create the Autoencoder network": [[62, "Create-the-Autoencoder-network"]], "Define model data": [[62, "Define-model-data"]], "Encoder/Decoder Setup": [[62, "Encoder/Decoder-Setup"]], "Training the encoder": [[62, "Training-the-encoder"]], "Reconstruction of the Data": [[62, "Reconstruction-of-the-Data"]], "Python and Hardware": [[63, "Python-and-Hardware"]], "Arduino Nano Board": [[63, "Arduino-Nano-Board"]], "Arduino Software": [[63, "Arduino-Software"]], "Setup your board": [[63, "Setup-your-board"]], "Select Firmata Sketch": [[63, "Select-Firmata-Sketch"]], "Communicating with the board": [[63, "Communicating-with-the-board"]], "Let the on-board LED blink": [[63, "Let-the-on-board-LED-blink"]], "Tunable output": [[63, "Tunable-output"]], "Creating an Oscilloscope": [[63, "Creating-an-Oscilloscope"]], "Project: YOUR PROJECT TITLE": [[64, "Project:-YOUR-PROJECT-TITLE"]], "Introduction": [[64, "Introduction"]], "Fundamentals": [[64, "Fundamentals"]], "Results and Discussion": [[64, "Results-and-Discussion"]], "Summary": [[64, "Summary"]], "NumPy arrays": [[65, "NumPy-arrays"]], "Creating Numpy Arrays": [[65, "Creating-Numpy-Arrays"]], "From lists": [[65, "From-lists"]], "Using array-generating functions": [[65, "Using-array-generating-functions"]], "linspace and logspace": [[65, "linspace-and-logspace"]], "mgrid": [[65, "mgrid"]], "diag": [[65, "diag"]], "zeros and ones": [[65, "zeros-and-ones"]], "Manipulating NumPy arrays": [[65, "Manipulating-NumPy-arrays"]], "Slicing": [[65, "Slicing"]], "Reshaping": [[65, "Reshaping"]], "Adding a new dimension: newaxis": [[65, "Adding-a-new-dimension:-newaxis"]], "Stacking and repeating arrays": [[65, "Stacking-and-repeating-arrays"]], "Tile and repeat": [[65, "Tile-and-repeat"]], "Concatenate": [[65, "Concatenate"]], "Hstack and vstack": [[65, "Hstack-and-vstack"]], "Applying mathematical functions": [[65, "Applying-mathematical-functions"]], "Operation involving one array": [[65, "Operation-involving-one-array"]], "Operations involving multiple arrays": [[65, "Operations-involving-multiple-arrays"]], "Add On: Making publication ready figures": [[66, "Add-On:-Making-publication-ready-figures"]], "Creating a plot with a specific bounding box size": [[66, "Creating-a-plot-with-a-specific-bounding-box-size"]], "Creating a plot with a specific axis frame size": [[66, "Creating-a-plot-with-a-specific-axis-frame-size"]], "Choosing fonts": [[66, "Choosing-fonts"]], "Plotting data": [[67, "Plotting-data"]], "Simple Plotting - Implicit Version": [[67, "Simple-Plotting---Implicit-Version"]], "Line Plot": [[67, "Line-Plot"]], "Axis Labels": [[67, "Axis-Labels"]], "Legends": [[67, "Legends"]], "Scatter plot": [[67, "Scatter-plot"]], "Histograms": [[67, "Histograms"]], "Combined plots": [[67, "Combined-plots"]], "Saving figures": [[67, "Saving-figures"]], "Plots with error bars": [[67, "Plots-with-error-bars"]], "Setting plotting limits and excluding data": [[67, "Setting-plotting-limits-and-excluding-data"]], "Masked arrays": [[67, "Masked-arrays"]], "Logarithmic plots": [[67, "Logarithmic-plots"]], "Semi-log plots": [[67, "Semi-log-plots"]], "Log-log plots": [[67, "Log-log-plots"]], "Arranging multiple plots": [[67, "Arranging-multiple-plots"]], "Contour and Density Plots": [[67, "Contour-and-Density-Plots"]], "Simple contour plot": [[67, "Simple-contour-plot"]], "Color contour plot": [[67, "Color-contour-plot"]], "Image plot": [[67, "Image-plot"]], "Additional Plotting - Explicit Version": [[67, "Additional-Plotting---Explicit-Version"]], "Plots with Multiple Spines": [[67, "Plots-with-Multiple-Spines"]], "Insets": [[67, "Insets"]], "Spine axis": [[67, "Spine-axis"]], "Polar plot": [[67, "Polar-plot"]], "Text annotation": [[67, "Text-annotation"]], "3D Plotting": [[67, "3D-Plotting"]], "Projection Scence": [[67, "Projection-Scence"]], "Line Plotting in 3D": [[67, "Line-Plotting-in-3D"]], "Surface Plotting": [[67, "Surface-Plotting"]], "Random numbers": [[68, "Random-numbers"]], "Uniformly distributed random numbers": [[68, "Uniformly-distributed-random-numbers"]], "Normally distributed random numbers": [[68, "Normally-distributed-random-numbers"]], "Exponentially distributed numbers": [[68, "Exponentially-distributed-numbers"]], "Random distribution of integers": [[68, "Random-distribution-of-integers"]], "Problem Set 2": [[69, "Problem-Set-2"]], "Input and output": [[70, "Input-and-output"]], "Keyboard input": [[70, "Keyboard-input"]], "Screen output": [[70, "Screen-output"]], "str.format() Formatting": [[70, "str.format()-Formatting"]], "%-Formatting": [[70, "%-Formatting"]], "f-Strings": [[70, "f-Strings"]], "File input/output": [[70, "File-input/output"]], "File I/O with NumPy": [[70, "File-I/O-with-NumPy"]], "Reading data from a text file": [[70, "Reading-data-from-a-text-file"]], "Writing data to a text file": [[70, "Writing-data-to-a-text-file"]], "File I/O with Pandas": [[70, "File-I/O-with-Pandas"]], "Short intro to Pandas": [[70, "Short-intro-to-Pandas"]], "Reading CSV data with Pandas": [[70, "Reading-CSV-data-with-Pandas"]], "Conditionals: if, elif, and else statements": [[71, "Conditionals:-if,-elif,-and-else-statements"]], "If example": [[71, "If-example"]], "If else example": [[71, "If-else-example"]], "If, elif, else example": [[71, "If,-elif,-else-example"]], "Combining conditions": [[71, "Combining-conditions"]], "For loops": [[71, "For-loops"]], "While loops": [[71, "While-loops"]], "Loops and array operations": [[71, "Loops-and-array-operations"], [74, "Loops-and-array-operations"]], "List comprehensions": [[71, "List-comprehensions"]], "Variables in functions": [[72, "Variables-in-functions"]], "Functions with more than one input or output": [[72, "Functions-with-more-than-one-input-or-output"], [74, "Functions-with-more-than-one-input-or-output"]], "Positional and keyword arguments": [[72, "Positional-and-keyword-arguments"], [74, "Positional-and-keyword-arguments"]], "Functions with variable number of arguments": [[72, "Functions-with-variable-number-of-arguments"]], "Unnamed functions (lambda function)": [[72, "Unnamed-functions-(lambda-function)"]], "Functions as arguments of functions": [[72, "Functions-as-arguments-of-functions"]], "Introduction to Computational Software": [[74, "Introduction-to-Computational-Software"]], "Table of Contents": [[74, "Table-of-Contents"]], "Lecture 3": [[74, "Lecture-3"]], "Conditionals": [[74, "Conditionals"]], "if, elif, and else statements": [[74, "if,-elif,-and-else-statements"]], "Logical Operators": [[74, "Logical-Operators"]], "for loops": [[74, "for-loops"]], "while loops": [[74, "while-loops"]], "List Comprehensions": [[74, "List-Comprehensions"]], "User-defined functions": [[74, "User-defined-functions"]], "Faster Array Processing": [[74, "Faster-Array-Processing"]], "Variable number of arguments": [[74, "Variable-number-of-arguments"]], "Numerical differentiation": [[74, "Numerical-differentiation"]], "More differentiation": [[74, "More-differentiation"]], "Classes and Objects": [[76, "Classes-and-Objects"]], "Definition of Classes": [[76, "Definition-of-Classes"]], "Class Methods": [[76, "Class-Methods"]], "The __init__ method": [[76, "The-__init__-method"]], "The __str__ method": [[76, "The-__str__-method"]], "Class and object variables": [[76, "Class-and-object-variables"]], "Brownian Motion": [[77, "Brownian-Motion"]], "Physics": [[77, "Physics"]], "Class Planning": [[77, "Class-Planning"]], "Simulating": [[77, "Simulating"]], "Plotting the trajectories": [[77, "Plotting-the-trajectories"]], "Characterizing the Brownian motion": [[77, "Characterizing-the-Brownian-motion"]], "Calculate the particle speed": [[77, "Calculate-the-particle-speed"]], "Calculate the particle mean squared displacement": [[77, "Calculate-the-particle-mean-squared-displacement"]], "Animations": [[78, "Animations"]], "Import Modules": [[78, "Import-Modules"]], "Particle class": [[78, "Particle-class"]], "Create a set of particles": [[78, "Create-a-set-of-particles"]], "Canvas and drawing function": [[78, "Canvas-and-drawing-function"]], "Threading for animation": [[78, "Threading-for-animation"]], "Numerical Differentiation": [[79, "Numerical-Differentiation"]], "First order derivative": [[79, "First-order-derivative"]], "Matrix version of the first derivative": [[79, "Matrix-version-of-the-first-derivative"]], "Second order derivative": [[79, "Second-order-derivative"]], "SciPy Module": [[79, "SciPy-Module"]], "Matrix version": [[79, "Matrix-version"]], "Numerical Integration": [[80, "Numerical-Integration"]], "Box method": [[80, "Box-method"]], "Trapezoid method": [[80, "Trapezoid-method"]], "Simpson method": [[80, "Simpson-method"]], "Solving ODEs": [[81, "Solving-ODEs"]], "Implicit Solution - Crank Nicholson": [[81, "Implicit-Solution---Crank-Nicholson"]], "Define Matrices": [[81, "Define-Matrices"]], "Use Initial Conditions": [[81, "Use-Initial-Conditions"]], "Explicit Solution - Numerical Integration": [[81, "Explicit-Solution---Numerical-Integration"]], "Euler Method": [[81, "Euler-Method"]], "Euler Cromer Method": [[81, "Euler-Cromer-Method"]], "Midpoint Method": [[81, "Midpoint-Method"]], "Putting it all together": [[81, "Putting-it-all-together"]], "The definition of the problem": [[81, "The-definition-of-the-problem"]], "Solving the problem": [[81, "Solving-the-problem"], [84, "Solving-the-problem"]], "Solving the Harmonic Oscillator in SciPy": [[81, "Solving-the-Harmonic-Oscillator-in-SciPy"]], "Definition": [[81, "Definition"], [81, "id3"], [83, "Definition"]], "Damped Driven Pendulum in SciPy": [[81, "Damped-Driven-Pendulum-in-SciPy"]], "Utilities": [[82, "Utilities"]], "COVID19": [[83, "COVID19"]], "The Kermack-McKendrick Model": [[83, "The-Kermack-McKendrick-Model"]], "Model Equation": [[83, "Model-Equation"]], "Real COVID19 numbers": [[83, "Real-COVID19-numbers"]], "Total number of cases": [[83, "Total-number-of-cases"]], "Number of Deaths": [[83, "Number-of-Deaths"]], "New cases per day": [[83, "New-cases-per-day"]], "Current cases": [[83, "Current-cases"]], "Coupled Pendula": [[84, "Coupled-Pendula"]], "Description of the problem": [[84, "Description-of-the-problem"]], "Sketch": [[84, "Sketch"]], "Equations of motion": [[84, "Equations-of-motion"], [87, "Equations-of-motion"]], "Setting up the function": [[84, "Setting-up-the-function"]], "Define initial parameters": [[84, "Define-initial-parameters"]], "Solve the equation of motion": [[84, "Solve-the-equation-of-motion"]], "Normal Modes": [[84, "Normal-Modes"]], "In-phase motion": [[84, "In-phase-motion"]], "Out-of-phase motion": [[84, "Out-of-phase-motion"]], "Beat case": [[84, "Beat-case"]], "Computation of energy (here for the beat case)": [[84, "Computation-of-energy-(here-for-the-beat-case)"]], "Potential energy of the pendula": [[84, "Potential-energy-of-the-pendula"]], "Potential energy of the spring": [[84, "Potential-energy-of-the-spring"]], "Kinetic energies": [[84, "Kinetic-energies"]], "Total energy": [[84, "Total-energy"]], "Total energy exchange of the pendula": [[84, "Total-energy-exchange-of-the-pendula"]], "Fourier Analysis": [[85, "Fourier-Analysis"]], "Fourier series": [[85, "Fourier-series"]], "Fourier transform": [[85, "Fourier-transform"]], "Frequency analysis of our coupled pendula": [[85, "Frequency-analysis-of-our-coupled-pendula"]], "Appendix: Fourier Analysis of a damped oscillation": [[86, "Appendix:-Fourier-Analysis-of-a-damped-oscillation"]], "Spring Pendulum": [[87, "Spring-Pendulum"]], "Physical Model": [[87, "Physical-Model"], [88, "Physical-Model"], [89, "Physical-Model"]], "Numerical Solution": [[87, "Numerical-Solution"], [88, "Numerical-Solution"], [89, "Numerical-Solution"]], "Initial parameters": [[87, "Initial-parameters"]], "Angle and Length over Time": [[87, "Angle-and-Length-over-Time"]], "Planetary Motion": [[88, "Planetary-Motion"]], "Initial Parameters: Planets": [[88, "Initial-Parameters:-Planets"]], "Solution: Planets": [[88, "Solution:-Planets"]], "Plotting: Planets": [[88, "Plotting:-Planets"]], "Trajectory": [[88, "Trajectory"]], "Energy": [[88, "Energy"]], "Diffusion equation": [[89, "Diffusion-equation"]], "Spatial derivative": [[89, "Spatial-derivative"]], "Temporal derivative": [[89, "Temporal-derivative"]], "Bringing all together": [[89, "Bringing-all-together"]], "Curve fitting": [[91, "Curve-fitting"]], "Idea": [[91, "Idea"]], "Least squares": [[91, "Least-squares"]], "Data": [[91, "Data"]], "Least square fitting": [[91, "Least-square-fitting"]], "\\chi-squared value": [[91, "\\chi-squared-value"]], "Residuals": [[91, "Residuals"]], "Covariance matrix": [[91, "Covariance-matrix"]], "Plane Waves": [[92, "Plane-Waves"]], "Equations": [[92, "Equations"], [93, "Equations"], [95, "Equations"]], "Electric field": [[92, "Electric-field"], [93, "Electric-field"]], "Plane wave propagation": [[92, "Plane-wave-propagation"]], "Imaginary wave vector": [[92, "Imaginary-wave-vector"]], "Interference of two plane waves": [[92, "Interference-of-two-plane-waves"]], "Plane wave at a boundary": [[92, "Plane-wave-at-a-boundary"]], "Fresnel equations": [[92, "Fresnel-equations"]], "Incident wave": [[92, "Incident-wave"]], "Reflected wave": [[92, "Reflected-wave"]], "Refracted wave": [[92, "Refracted-wave"]], "Spherical waves": [[93, "Spherical-waves"]], "Plot the intensity in an image plane": [[93, "Plot-the-intensity-in-an-image-plane"]], "Interference between a spherical and a plane wave": [[93, "Interference-between-a-spherical-and-a-plane-wave"]], "Huygens principle": [[94, "Huygens-principle"]], "Diffraction pattern of a single slit": [[94, "Diffraction-pattern-of-a-single-slit"]], "Farfield vs. nearfield": [[94, "Farfield-vs.-nearfield"]], "Comparison to the analytical solution": [[94, "Comparison-to-the-analytical-solution"]], "Gaussian Beam": [[95, "Gaussian-Beam"]], "Intensity plot": [[95, "Intensity-plot"]], "Intensity profiles": [[95, "Intensity-profiles"]], "Assignments": [[4, "assignments"]], "Assignment Rules": [[4, "assignment-rules"]], "Resources": [[7, "resources"]], "Molecular Nanophotonics Group": [[7, "molecular-nanophotonics-group"]], "Additional Advanced Courses": [[7, "additional-advanced-courses"]], "Python Documentation": [[7, "python-documentation"]], "Python Tutorials": [[7, "python-tutorials"]], "Julia Tutorial": [[7, "julia-tutorial"]], "Pluto NoteBook": [[7, "pluto-notebook"]], "Exercise 1": [[13, "exercise-1"]], "Introduction to Jupyter": [[38, "Introduction-to-Jupyter"]], "What is Jupyter Notebook?": [[38, "What-is-Jupyter-Notebook?"]], "Notebook editor": [[38, "Notebook-editor"], [39, "Notebook-editor"], [42, "Notebook-editor"]], "Kernels": [[38, "Kernels"]], "Notebook documents": [[38, "Notebook-documents"]], "Exam": [[5, "exam"]], "Mechanics": [[5, "mechanics"]], "Thermodynamics/Statistical Physics": [[5, "thermodynamics-statistical-physics"]], "Optics": [[5, "optics"]], "Electrodynamics": [[5, "electrodynamics"]], "Course Schedule": [[8, "course-schedule"]], "Edit mode": [[39, "Edit-mode"], [42, "Edit-mode"]], "Command mode": [[39, "Command-mode"], [42, "Command-mode"]], "Keyboard navigation": [[39, "Keyboard-navigation"], [42, "Keyboard-navigation"]], "Running code in your notebook": [[39, "Running-code-in-your-notebook"]], "Managing the kernel": [[39, "Managing-the-kernel"], [42, "Managing-the-kernel"]], "Running code": [[42, "Running-code"]]}, "indexentries": {}})
\ No newline at end of file
diff --git a/source/course-info/.ipynb_checkpoints/exam-checkpoint.rst b/source/course-info/.ipynb_checkpoints/exam-checkpoint.rst
index 6546056..5aad795 100644
--- a/source/course-info/.ipynb_checkpoints/exam-checkpoint.rst
+++ b/source/course-info/.ipynb_checkpoints/exam-checkpoint.rst
@@ -31,7 +31,7 @@ Grading: Notebooks will be graded based on:
 - quality of the plots (axis labels, readability of the labels)
 - use of concepts we used for the notebooks (use of markdown, multiple code cells )
 
-The deadline for handing in the project is **September 4, 2024** 
+The deadline for handing in the project is **September 4, 2024, at 1pm sharp! Do not miss the deadline!!!!!!**
 
 Please submit your projects via email to Andrea Kramer,  **firstname.surname@uni-leipzig.de**.
 
diff --git a/source/course-info/exam.rst b/source/course-info/exam.rst
index 6546056..5aad795 100644
--- a/source/course-info/exam.rst
+++ b/source/course-info/exam.rst
@@ -31,7 +31,7 @@ Grading: Notebooks will be graded based on:
 - quality of the plots (axis labels, readability of the labels)
 - use of concepts we used for the notebooks (use of markdown, multiple code cells )
 
-The deadline for handing in the project is **September 4, 2024** 
+The deadline for handing in the project is **September 4, 2024, at 1pm sharp! Do not miss the deadline!!!!!!**
 
 Please submit your projects via email to Andrea Kramer,  **firstname.surname@uni-leipzig.de**.