Introduction to Mathematical Physics II | Department of Physics

Introduction to Mathematical Physics II

1. Functions of a complex variable 
(a) Elementary properties of analytic functions 
(b) Integration in the complex plane 
(c) Analytic functions 
(d) Calculus of residues: applications 
(e) Periodic functions: Fourier series 
(f) Gamma function 

2. Differential Equations: analytical methods 
(a) Linear differential equations and their power series solutions 
(b) Legendre’s equation 
(c) Bessel’s equation 
(d) Hypergeometric equation 

3. Hilbert Spaces 
(a) Infinite-dimensional vector spaces 
(b) Function spaces 
(c) Fourier series 
(d) Fourier integral and integral transforms 
(e) Orthogonal polynomials 

4. Partial differential equations 
(a) Linear first-order equations 
(b)The Laplacian and the Green function for Laplace’s equation 
(c) Time-dependent partial differential equations: The diffusion 
equation and the Schrödinger equation 
(d) Nonlinear partial differential equations and solitons

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