Lecture Notes for PHYS:4762 Mathematical Methods of Physics II
Below are links to the scanned PDF versions of the lecture notes handed out in class:
- Lecture #1: Complex Variable Theory and Cauchy's Integral Theorem
- Lecture #2: Cauchy's Integral Formula, Laurent Expansions, and Singularities
- Lecture #3: Branch Cuts, Analytic Continuation, and Residue Theorem
- Lecture #4: Evaluation of Definite Integrals by Contour Integration
- Lecture #5: Evaluation of Sums and Other Topics in Complex Analysis
- Lecture #6: Orthogonal Polynomials, Bernoulli Numbers, and Euler-MacLaurin Formula
- Lecture #7: Dirichlet Series, Infinite Products, Asymptotic Series, and Method of Steepest Descent
- Lecture #8: Dispersion Relations and Bessel Functions
- Lecture #9: Bessel Functions, Orthogonality, and Neumann Functions
- Lecture #10: Hankel Functions, Modified Bessel Functions, and Asymptotic Expansions
- Lecture #11: Spherical Bessel Functions And Legendre Functions
- Lecture #12: Legendre Functions" Orthogonality, Generating Function, and Associated Legendre Equation
- Lecture #13: Associated Legendre Functions, Spherical Harmonics, and Second Kind
- Lecture #14: Fourier Series
- Lecture #15: Gibbs Phenomenon, Integral Transforms, and Fourier Transforms
- Lecture #16: Fourier Transforms: Properties and Convolutions
- Lecture #17: Convolution Theorem, Signal Processing, and Discrete Fourier Transforms
- Lecture #18: Laplace Transforms
- Lecture #19: Laplace Transforms: More Properties anc Convolution Theorem
- Lecture #20: Inverse Laplace Transforms and Integral Equations
- Lecture #21: Methods for Solving Integral Equations
- Lecture #22: Hilbert-Schmidt Theory and Interoduction to Calculus of Variations
- Lecture #23: Calculus of Variations and Hamilton's Equations
- Lecture #24: Lagrangian Multipliers
- Lecture #25: Mutilple Timescale Methods