Linear Partial Differential Equations and Fourier Theory
by Marcus Pivato
Publisher: Cambridge University Press 2005
Number of pages: 619
This is a textbook for an introductory course on linear partial differential equations and initial/boundary value problems. It also provides a mathematically rigorous introduction to basic Fourier analysis, which is the main tool used to solve linear PDEs in Cartesian coordinates. Finally, it introduces basic functional analysis. This is necessary to rigorously characterize the convergence of Fourier series, and also to discuss eigenfunctions for linear differential operators.
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by Christopher Frye, Costas J. Efthimiou - arXiv
The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to physics or mathematics undergraduates.
by H. S. Carslaw - Macmillan and co.
An introductory explanation of the theory of Fourier's series. It covers tests for uniform convergence of series, a thorough treatment of term-by-term integration and second theorem of mean value, enlarged sets of examples on infinite series, etc.
by Thomas Wolff - American Mathematical Society
An inside look at the techniques used and developed by the author. The book is based on a graduate course on Fourier analysis he taught at Caltech. It demonstrates how harmonic analysis can provide penetrating insights into deep aspects of analysis.
by Terence Tao, Christoph Thiele - arXiv
The nonlinear Fourier transform is the map from the potential of a one dimensional discrete Dirac operator to the transmission and reflection coefficients thereof. Emphasis is on this being a nonlinear variant of the classical Fourier series.