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Intermediate Mathematical Physics—PHYS 4112
This course introduces the topics of tensor analysis, special functions, Legendre, Bessel, Hermite, Laguerre functions, and partial differential equations.
Required Textbook: Mathematical Methods in the Physical Sciences, Third Edition by Mary Boas
Required software: Mathematica
Course grade: 100% homework
Syllabus:
Chapter 10: Tensor Analysis
Chapter 11: Special Functions
Chapter 12: Legendre, Bessel, Hermite, and Laguerre functions
Chapter 13: Partial Differential Equations
Office Hours: 1:30pm - 2:30pm Tues., Wed. in Nicholson 447
Homeworks
Homework 12 due Thursday, November 29 in class
Homework 11 due Wednesday, November 21 by 4pm in Nicholson 447
Homework 10 due Thursday, November 15 in class
Homework 9 due Thursday, November 1 in class
Homework 8 due Thursday, October 25 in class
Homework 7 due Thursday, October 18 in class
Homework 6 due Thursday, October 11 in class
Homework 5 due Wednesday, October 3 by 4pm in Nicholson 447
Homework 4 due Thursday, September 20 in class
Homework 3 due Thursday, September 13 in class
Homework 2 due Thursday, September 6 in class
Homework 1 due Thursday, August 30 in class
Lectures
Lecture 26: Solving wave equation for a vibrating string PDF
Lecture 25: Solving Schrodinger's equation for particle in a 2D box PDF
Lecture 24: introduction to partial differential equations and solving Laplace's equation PDF
Lecture 23: quantum harmonic oscillator and Hermite functions and polynomials PDF
Lecture 22: orthogonality of Bessel functions and the theorem of Fuchs PDF
Lecture 21: more about Bessel functions and the quantum bouncing ball PDF
Lecture 20: properties of Bessel functions and generalized Bessel equation PDF
Lecture 19: Solving Bessel's differential equation using generalized power series PDF
Lecture 18: generalized power series and introduction to Bessel functions PDF
Lecture 17: Legendre series, least-squares polynomial fit, associated Legendre functions PDF
Lecture 16: orthonormality of Legendre polynomials PDF
Lecture 15: generating function for Legendre polynomials and application to approximating potentials PDF
Lecture 14: Leibniz rule for differentiation and Rodrigues formula for Legendre polynomials PDF
Lecture 13: Series solutions of differential equations, Legendre polynomials PDF
Lecture 12: Elliptic integrals and the simple pendulum PDF
Lecture 11: Asymptotic series and expansions, Stirling's formula PDF
Lecture 10: Beta function and the simple pendulum, Gaussian error function PDF
Lecture 9: Gamma and Beta functions PDF
Lecture 8: Vector operators in orthogonal curvilinear coordinates PDF
Lecture 7: Curvilinear coordinates PDF
Lecture 6: Pseudovectors and pseudotensors, proper and improper rotations, cross product PDF
Lecture 5: Manipulations with Levi-Civita symbol and dual tensor PDF
Lecture 4: Examples of moment of inertia tensor: two point masses and octant of sphere, Levi-Civita symbol PDF
Lecture 3: Moment of inertia tensor, principal moments, and principal axes PDF
Lecture 2: Cartesian vectors, Cartesian tensors, outer product, Einstein summation convention, tensor contractions PDF
Lecture 1: introduction to course, tensor analysis, stress tensor, tensor as a physical quantity, rotation matrices, Cartesian tensors PDF
Last modified: December 29, 2018.
