Mathematical Methods in Physics
PHGN 511
Mathematical Methods in Physics
Fall 2021
The Facts:

 Me: aflourno@mines.edu
 Lecture: T/TR 5:006:15pm in CK150
 Required text: "Mathematics of Classical and Quantum Physics" by Frederick Byron and Robert Fuller.
 Office Hours: Tuesday 1:301:50pm, Wednesday 12:50pm and 56:20pm
 Evaluation: Your grade will be based on lecture participation (10%), homework (40%), an inclass midterm exam (20%) and a takehome final exam (30%).
Lecture participation will be assessed by your response to questions posed during lecture. I will draw names randomly to answer questions and if you are not present or fail to respond as if paying attention, you will lose 1% of the 10% for lecture participation. Any student sitting in on the course (not enrolled) will be expected to take part in lecture participation or asked to refrain from attending.
Homework will be assigned regularly and "due" on Thursdays. Instead of turning in your assignments I will administer short homework quizzes.
The quiz will consist of two questions from which you will choose one to answer. Each question will be very similar to a part of one of the homework problems, but not identical.
You will be allowed to use your homework solutions to help you on the quiz, but not your book. If you are a good then perhaps you will be able to work the quiz problems on the fly, but with the time constraint this will be nexttoimpossible for most, so you should try your best to complete the assignments on your own. The reasons for this are twofold. First it cuts out the motivation for simply copying someone else's homework, and secondly it will make the grading more expedient.
Description:
This course is in flux. While the old version served as a basis for the math that would be used in the other four courses, a new version, to be implemented next year, will provide the math basis as well as cover topics in the no longer present Classical Mechanics course (to be replaced by a lab course next year). While this year is still part of the old scheme, I am looking to make some adjustments.
Objectives:
Our goal will be to start with a more mathematical analysis of vector spaces, beginning with the finite dimensional cases (applying the results to space and spacetime), then moving onto the infinitedimensional cases (applying the results to quantum mechanics). Topics among these include abstract definitions and theorems, the idea of bases, transformations, innerproducts, and classifications of operators and their properties. We will then move onto anayltic function theory, and study the power of complex variables. After that we will look at solutions generating techniques such as Green's functions and perturbation theory. In the end (or perhaps earlier) we will go over aspects of group theory as applied to physics.
Lectures:
I will point out relevant sections of the suggested text for further reading. After each lecture, I will post my notes below as well.
 Lecture 8/24 (3.13.3): Introduction to the Course and a Definition of Vector Spaces Lecture Notes Lecture Video
 Lecture 8/26 (3.43.7): Isomorphisms and Linear Operators with their Inverses and Matrix Realizations Lecture Notes Lecture Video
 Lecture 8/31 (3.83.9): Matrices and Coordinate Changes, then the Determinant Quest for an Inverse Lecture Notes Lecture Video
 Lecture 9/2 (3.10): Mr. Eigen Lecture Notes Lecture Video
 Lecture 9/7 (4.14.3): Innards Lecture Notes Lecture Video
 Lecture 9/9 (4.4): Inner Product Weighs in on Determinant and Self Adjoint Operators Lecture Notes Lecture Video
 Lecture 9/14 (4.54.7): Isometries, the Big Picture and the Normal One, and their Diagonalization Lecture Notes Lecture Video
 Lecture 9/16 (4.8,4.9): A Sample of Their Uses Lecture Notes Lecture Video
 Lecture 9/21 (4.11): Time to get Perturbed Lecture Notes Lecture Video
 Lecture 9/23 (4.12): Degenerately Perturbed Lecture Notes Lecture Video
 Lecture 9/28 (5.1): To Infinity and Beyond Lecture Notes Lecture Video
 Lecture 9/30 (5.2): The Completeness of Infinity Lecture Notes Lecture Video
 Lecture 10/5 (5.3,5.4): The Dirac Spike and Polynomial Goodness Lecture Notes Lecture Video
 Lecture 10/7 (5.5, 5.9, 5.10): Legendre, Laguerre and Hermite walk into a bar... Lecture Notes Lecture Video
 Lecture 10/12 (5.6): WTF: What The Fourier? Lecture Notes Lecture Video
 Lecture 10/21 (5.7,5.8): More Fourier and his Marriage to Legendre Lecture Notes Lecture Video
 Lecture 10/26 (5.11): Quantum Mechanics Lecture Notes Lecture Video
 Lecture 10/28 (5.11): Quantum Mechanics continued... Lecture Notes Lecture Video
 Lecture 11/2 (6.16.2): An Analytical Analysis of Analytical Stuff Lecture Notes Lecture Video
 Lecture 11/4 (6.36.5): Integrating the Analytical Stuff Lecture Notes Lecture Video
 Lecture 11/9 (6.7): Expanding Into the Unknown Lecture Notes Lecture Video
 Lecture 11/11 (6.86.9): The Residue and an Introduction to Mr. Green Lecture Notes Lecture Video
 Lecture 11/16 (7.37.4): Green and Dirac walk into a Delta in 1D! Lecture Notes Lecture Video
 Lecture 11/18 (7.4 and 7.8): Green's Paint Applied to 3D! Lecture Notes Lecture Video
 Lecture 11/23: Spaces and Vector Spaces Lecture Notes Lecture Video
 Lecture 12/2: The Discrete vs. Continuous Stories of Groups Lecture Notes Lecture Video
 Lecture 12/7: I Won't Lie, This One Is The Best Lecture Notes Lecture Video
Homework:
Exams: