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spin:esc201_hs2021

Simulations in the Natural Sciences I

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)

Corona Virus Measures

Dear Students,

Video lectures will be available (see below).

Exercises will take place via Microsoft Teams :ESC 201

Joachim Stadel


Video Lectures

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

ESC201 Video downloads

Lectures

Assignments

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):

  1. The working python source code
  2. The requirements.txt file for your virtual environment (if you used a 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

List of assignments

  1. 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 xx - 100 = 0)! (to submit by 3 October 20201, 9pm)
  2. 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)
  3. 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)
  4. 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)
  5. 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).
  6. 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