ESC201:Fall 2020: Monday Lecture: 13:00-14:00 Exercises: 14:00-17:00 in online only

TAs: Stefan Schafroth, Sebastian Schulz (sebastian.schulz@uzh.ch), Peter Espenshade (peter.espenshade@uzh.ch)

Dear Students, I will provide a video lectures from the second class onwards, the 21. September 2020. Exercises will in future take place via Microsoft Teams :ESC 201

Joachim Stadel

Videos for the lectures can be found here (they are too large for my Wiki):

ESC201 Video downloads

14. Sep. 2020: First Lecture

21. Sep. 2020: Bisection Method, Newton's Method, Kepler's Equation

28. Sep. 2020: Population growth, Chaos and Fractals

5. Oct. 2020: Fractals from complex numbers, Start of ODEs

12. Oct. 2020: Ordinary differential equations, Lotka-Voltera System

19. Oct. 2020: Symplectic Integrators: Leap-frog

26. Oct. 2020: Gravitation for Many Bodies: a Digital Orrery

2. Nov. 2020: Laplace Equation, Jacobi and SOR Methods

Should be handed in every Sunday night by 21:00 following the Monday lecture. Assignments should be individual and should be in python and provide a correct virtual environment!

For help getting started with virtual environments, please read carefully Python Virtual Environments for Pip and Python Virtual Environments for Conda.

You should email 3 things to Peter (peter.espenshade@uzh.ch):

1. The working python source code
2. The requirements.txt file for your virtual environment
3. A .pdf or .png image or animation of the output of your program

Template: template.zip

Instructions:

Please add the names of the people you work together (if you do) to the comment section of your python scripts.

Create a virtual environment using

Pip

- run virtualenv yourenv_name to create a virtual environment

- run source yourenv_name/bin/activate to activate yourenv_name

- install necessary libraries that you want using pip install package_name

- work in that directory, get your outputs (*.pdf, *.png, *jpeg, *.mp4, etc…)

- run pip freeze > requirements.txt to get your list of libraries

Conda

- run conda create -n yourenvname python=x.x anaconda to create a virtual environment

- run source activate yourenvname to activate yourenv_name

- install necessary libraries that you want using conda install -n yourenv_name package_name

- work in that directory, get your outputs (*.pdf, *.png, *jpeg, *.mp4, etc…)

- run conda list –export > requirements.txt to get your list of libraries

1. Kepler's equation: Draw/Animate a plot showing the elliptical orbit about the sun/star by repeatedly solving Kepler's equation using Newton's Method (due 27 September, 2020).
2. Logistic equation and chaos: Draw a Feigenbaum diagram that results from solving the logistic equation (due 4 October, 2020). (Optional: Draw the iterations of the logistic equation in a x_(n+1) vs x_n plot.)
3. Fractals using complex numbers: Draw the Mandelbrot set as presented in the lecture (due 11 October, 2020). (Optional: Draw some Julia sets with various c.)
4. Ordinary Differential Equations: Solve the Lotka-Volterra equation using the Euler method and the midpoint Runge-Kutta method (optional: 4th order Runge Kutta method) and compare the results. Make two plots: the time dependence of both populations (mice and foxes), and the phase diagram using different initial conditions (due 18 October, 2020).
5. Symplectic Integrators: Use the Leap-Frog method to make a phase plot (p vs q) of the harmonic oscillator for different total energies. Make the same plot for a simple pendulum (due 25 October, 2020).
6. Solar System Orrery Initial Conditions , Loading Script (due 1 November, 2020)
7. Elliptical partial differential equations: Solve the Poisson equation for the electromagnetic potential using the SOR method described in the lecture, with boundary conditions given by a 1000 Volt stick in the center of a 0 Volt box (as depicted in the lecture notes). Plot the contours of the resulting potential (due 8 November, 2020).