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Author(s): D. B. Skinner, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part IB Lecture Notes
Publisher: University of Cambridge
Year: 2015

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; mathematical methods; numerical methods

Introduction
Vector spaces
Fourier series
Fourier series
Convergence of Fourier series
Differentiability and Fourier series
Sturm-Liouville Theory
Sturm-Liouville operators
Least squares approximation
Partial differential equations
Laplace's equation
Laplace's equation in the unit disk in R2
Separation of variables
Laplace's equation in spherical polar coordinates
Laplace's equation in spherical polar coordinates
Legendre Polynomials
Solution to radial part
Multipole expansions for Laplace's equation
Laplace's equation in cylindrical coordinates
The heat equation
The wave equation
Distributions
Distributions
Green's functions
Green's functions for initial value problems
Fourier transforms
The Fourier transform
The Fourier inversion theorem
Parseval's theorem for Fourier transforms
A word of warning
Fourier transformation of distributions
Linear systems and response functions
General form of transfer function
The discrete Fourier transform
The fast Fourier transform*
More partial differential equations
Well-posedness
Method of characteristics
Characteristics for 2nd order partial differential equations
Green's functions for PDEs on Rn
Poisson's equation