Mathematical Methods in Physics

PHGN 511
Mathematical Methods in Physics
Fall 2021


The Facts:

  • Me: aflourno@mines.edu
  • Lecture: T/TR 5:00-6:15pm in CK150
  • Required text: "Mathematics of Classical and Quantum Physics" by Frederick Byron and Robert Fuller.
  • Office Hours: Tuesday 1-1:50pm, Wednesday 1-2:50pm and 5-5:50pm
  • Evaluation: Your grade will be based on lecture participation (10%), homework (40%), an in-class 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 next-to-impossible for most, so you should try your best to complete the assignments on your own. The reasons for this are two-fold. 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 infinite-dimensional cases (applying the results to quantum mechanics). Topics among these include abstract definitions and theorems, the idea of bases, transformations, inner-products, 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.

Homework:


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