spin:esc201_hs2021

**ESC201:**Fall 2021: Monday Lecture: 13:00-14:00 Exercises: 14:00-17:00 in **online only**

**TAs**: Stefan Schafroth, Sebastian Schulz (**sebastian.schulz@uzh.ch**), Noah Kubli (**noah.kubli@uzh.ch**)

**
Dear Students,
**

Video lectures will be available (see below).

Exercises will take place via Microsoft Teams :ESC 201

Joachim Stadel

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

20. Sep. 2021: First Lecture

27. Sep. 2021: Newton's Method and Kepler's Equation

4. Oct. 2021: Population Growth, Chaos and Fractals

11. Oct. 2021: Complex Fractals, Start of ODEs

18. Oct. 2021: Ordinary Differential Equations: Predator-Prey

25. Oct. 2021: Symplectic Integrators: Leap-frog and the Simple Pendulum

Your solutions should be handed in 13 days after each assignment has been given, i.e. **Sunday night by 21:00** two weeks after the Monday lecture.
Assignments should be **individual** and should be in python and **provide a
correct virtual environment!** (if you stick to standard libraries like numpy, matplotlib, scipy… **you can also just submit your python source code together with the output** of your program)

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 Sebastian (**sebastian.schulz@uzh.ch**):

- The working
**python source code** - The
**requirements.txt**file for your virtual environment (if you used a virtual environment) - 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

- Implement the bisection root finding method presented in the first lecture for a function f of your choice (e.g. f(x) = ax³ + bx² + cx + d, or x
^{x}- 100 = 0)! (**to submit by 3 October 20201, 9pm**) - Plot (and/or animate) the elliptical orbit of a planet around the sun by repeatedly solving Kepler's equation with Newton's method (or the bisection method), as explained in the lecture! (
**to submit by 10 October 2021, 9pm**) - Draw a Feigenbaum diagram that results from solving the logistic equation (
**to submit by 17 October, 2021, 9pm**). (Optional: Implement a function that allows you to zoom into the Feigenbaum diagram) - Fractals: Draw some Julia sets with various constants c (you can start with the Mandelbrot set as it was explained in the lecture and the exercise class)! (
**to submit by 24 October, 2021, 9pm**) - 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 (
**to submit by 31 October, 2021, 9pm**). - Symplectic Integrators: Use the Leap-Frog method to make a phase plot (p vs q) of the harmonic oscillator for different total energies. Compare the results with what you get using the Forward Euler method and the midpoint Runge-Kutta method. Make the same plot for a simple pendulum (
**to submit by 7 November, 2021, 9pm**).

spin/esc201_hs2021.txt · Last modified: 2021/10/25 14:33 by stadel

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International