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

Homework Points
Interaction on own project
Category	min per person	point factor	max points
Commits	6	1	6
Merge requests	3	1	3
Merge Accepted	1	1	1
Branches	2	0.5	1
Issues	10	0.5	5
Closed Issues	5	0.2	1
# Conversations	30	0.2	6
Total			23
Shared project points
# Label	5	0.2	1
# Milestones	2	1	2
# Tags	0	1	0
Total	7		5
Interaction on others project(s)
Category	min per person	point factor	max points
Commits	3	1	3
Branches	1	0.5	0.5
Issues	9	0.5	4.5
# Conversations	15	0.2	3
Total	22		11
Result
Task completion	5	1	5
Sum			42