Homework Task

Check out https://github.com/ubsuny/CompPhys/Calculus and generate a library calculus.py with functions / methods needed for Task 1 and 2.

In particular fullfill three tasks (one for each group member):

Task 1: Use the four integral algorithms (simpson, adaptive trapezoid, trapezoid) to create a Jupyter notebook that imports the functions from calculus.py and use them to calculate and plot the integral of:

• $\exp(-1/x)$
• $\cos(1/x)$
• $x^3 + \frac 1{\textrm{GroupNumber}}$

with different boundaries:

$$ [0,10\cdot\textrm{GroupNumber}],]0,\pi\cdot\textrm{GroupNumber}],[-1,1] $$

(Pay attention to the boundary brackets ][)

Additionally, compare the accuracies (how many digits are correct) and efficiencies (how many steps does it take to reach a given accuracy).

Task 2: Compare the accuracies (how many digits are correct) and efficiencies (how many steps does it take to reach a given accuracy) for any two root-finding algorithms on the two functions

$$ y(x) = \tan(x) \textrm{ and} $$

$$ y(x) = \tanh(x). $$

Task 3:

• Compare the numpy integration functions to the ones found in compphys
• Add missing docstrings in calculus.py
• Reuse github actions for linting and unit tests for calculus.py
• write unit tests for functions in calculus.py

For this you have to complete the following steps:

• Discuss in this repository using issues who will do which task (specified above)
• Discuss who should be the main responsible for the repository (the one that can accept merge requests, let me know in discord so I can adjust rights)
• Work together by generating calculus.py with functions for task 1 and 2 from compphys
• Discuss and generate milestone for your project to optimize the timeline of your project
• Discuss and generate labels for your issues
• Fork this repository
• Merge the necessary fies from the original homework project into your fork
• commit
• create merge requests for your work

Also use discord for discussing solutions to any issues popping up.

Grading