Dreyer-Research-Group

PHY 604: Computational Methods in Physics and Astrophysics II

Instructor: Cyrus Dreyer, Physics B104, cyrus.dreyer@stonybrook.edu
*Office Hours: By appointment
Syllabus

Lectures, example programs, readings, etc.

Lecture 1: Intro and basics of computation

• Lecture 1 slides
• Readings:
• What every computer scientist should know about floating-point arithmetic
• Wikipedia page on the Floating Point
• Wikipedia page on the Kahan Summation Algorithm
• Example programs:
• Fortran program for calcuating factorial
• Python program for calcuating factorial
• Fortran program for finding machine $\epsilon$
• Python program for converting decimal to binary

Lecture 2: Good programming practices

• Lecture 2 slides
• Readings:
• Pro Git book
• Fortran best practices
• Good enough practices in scientific computing
• Example programs:
• Python program for matrix inversion including unit test

Lecture 3: Good practices and numerical differentiation

• Lecture 3 slides
• Readings:
• Wikipedia page on finite difference coefficients
• Wikipedia page on Make
• Blog on numerical differentiation
• Example programs:
• Fortran makefile example

Lecture 4: Numerical integration

• Lecture 4 slides
• Example programs:
• Jupyter notebook exploring numerical integration of Fresnel function

Lecture 5: Interpolation

• Lecture 5 slides
• Readings:
• Wikipedia article on Chebyshev nodes
• Myths about polynomial interpolation
• Example programs:
• Jupyter notebook exploring Lagrange Polynomial interpolation
• Jupyter notebook exploring cubic splines

Lecture 6: Splines and root finding

• Lecture 6 slides
• Readings:
• Wikipedia page on root finding
• Example programs:
• Jupyter notebook exploring cubic splines
• Jupyter notebook implementing an example of the Newton-Raphson method

Lecture 7: Ordinary Differential Equationss

• Lecture 7 slides
• Readings:
• Example programs:
• Jupyter notebook solving orbital ODEs with different methods

Lecture 8: More on ODEs

• Lecture 8 slides
• Readings:
• Example programs:
• Jupyter notebook solving orbital ODEs with the Bulirsch-Stoer method
• Jupyter notebook solving thrown ball boundary value problem using the shooting method
• Jupyter notebook solving one-dimensional Schrodinger equation in square well

Lecture 9: Finishing ODEs, start Linear Algebra

• Lecture 9 slides
• Readings:
Newman Ch. 6
Garcia Ch. 4
Pang Sec. 5.3
• Example programs:
• Jupyter notebook exploring matrix manipulations
• Jupyter notebook implementing Gauss elimination

Lecture 10: More on linear algebra, LU decomposition and iterative methods

• Lecture 10 slides
• Example programs:
• Jupyter notebook implementing the Jacobi iterative method
• Jupyter notebook using Newton's method for the Lorenz problem

Lecture 11: QR decomposition and nonlinear algebra

• Lecture 11 slides
• Readings:
Newman Ch. 6
Garcia Ch. 4
Pang Ch. 5
• An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
• Example programs:
• Jupyter notebook implementing QR decomposition for eigenvalue problems
• Jupyter notebook implementing steepest descent algorithm
• Jupyter notebook using Newton's method for the Lorenz problem

Lecture 12: Fourier analysis

• Lecture 12 slides
• Readings:
Newman Ch. 7
Wikipedia page on discrete Fourier transform
• Example programs:
• Jupyter notebook implementing discrete Fourier transform
• Jupyter notebook implementing fast Fourier transform

Lecture 13: FFTs and fitting

• Lecture 13 slides
• Readings:
Garcia Sec. 5.1
Wikipedia page on variance
Wikipedia page on propagation of uncertainty
• Example programs:
• Jupyter notebook on least-squares fitting
• Jupyter notebook implementing fast Fourier transform

Homeworks

Homework 1 (Due 09/17/25)

• Homework 1
• Instructions

Homework 2 (Due 10/01/25)

• Homework 2
• Instructions

Homework 3 (Due 10/22/25)

• Homework 3
• Instructions