This book is a carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.

Autorentext

Anders Vretblad is Senior Lecturer of Mathematics at Uppsala University, Sweden.

Inhalt

Introduction Preparations Laplace and Z Transforms Fourier Series L^2 Theory Separation of Variables Fourier Transforms Distributions Multi-Dimentional Fourier Analysis Appendix A: The ubiquitous convolution Appendix B: The Discrete Fourier Transform Appendix C: Formulae Appendix D: Answers to exercises * Appendix E: Literature