Computational Physics Course Materials

This repository contains materials from an upper-level undergraduate / intro graduate computational physics course taught remotely in Spring 2021 at Washington University in St. Louis. The course was taught in python, and so this repo predominantly contains lecture notes, example python notebooks, and both written and python course assignments. The course syllabus contains a general overview, but was not strictly followed, so more details are provided in this readme. The course introduces many topics, and dives deeper into a few. Basic ideas of different topics were typically introduced in a longer lecture, and a high-level overview of advanced ideas in a short followup lecture. Fully expanding on these topics could easily fill several courses! Many of these assignments and examples draw from the computational physics course at CWRU.

Lectures

The lectures predominantly contains notes from weekly class lectures (ranging from half-hour to 1.5 h) as raw text files, actual lecture notes presented during lectures in the onenote subdirectory, and python notebook examples in the notebooks subdirectory.

Assignments

Class assignments included:

• Written homework
• Coding homework
• Exams
• In-class exercises (labs)

My favorite exam problem was problem 2 on exam 1, which demonstrates a leading-order equivalence between Taylor expansions, polynomial interpolation, and curve fitting.

My favorite lab assignment involved solving the Gray-Scott reaction-diffusion equations, which resulted in some nice visuals.

Overview

Class	Notes	Brief Description	Examples Codes	Assignments
Class 1	Lec 1	When are computational methods useful?	Arrays, vectors, and such	---
Class 2	Lec 2	Some sources of numerical error	Demo	---
Class 3	Lec 3	Optimization: 1d root finding, min/max, and interpolation	Min/max, Root finding, Interpolation	---
Class 4	Lec 4	Min/max, interpolation in >1d, extrapolation	Demo	---
Class 5	Lec 5	Solving linear systems and Eigenstuffs	Linear solvers, Eigensystems	---
Class 6	Lec 6	SVD	Demo	---
Class 7	Lec 7	Least-squares fitting and splines, Chi-square	Demo	---
Class 8	Review	Class 1-7 Review		Exercises
Class 9	Lec 9	Intro to ODE solving	Demo	---
Class 10	Lec 9	More ODEs: Runge-Kutta, bounary-value methods	Richardson Extrapolation	---
Class 11	Lec 11	Error growth and stability, quadrature	Quadrature	---
Class 12	Class 12	More on error, more on quadrature	---	---
Class 13	Lec 13	Time for PDE solving! Finite differencing and IVPs	Demo	---
Class 14	Lec 14	FD method stability	---	---
Class 15	Lec 15	More on PDE stability	---	---
Class 16	Lec 16	Elliptic PDEs	---	---
Class 17	Review	Class 9-16 Review	---	Exercises
Class 18	Lec 18	Intro to FFTs, Convolutions	Demo	---
Class 19	Lec 19	More FFTs, correlations	Demo	---
Class 20	Lec 20	Randomness, probability (MC, PDFs)	Markov chains, Markov chains 2, Ising model	---

Some additional notes on PDE stability analysis are tex'd up. Some examples of symbolic computing are here, and a quick Mathematica intro (it has advantages over Python for many things) is here. Quick examples of how to optimize code performance in python are here.