Beschreibung:
This book presents the basic ideas in Fourier analysis and its applications to the study of partial differential equations. It also covers the Laplace and Zeta transformations and the fundaments of their applications. The author has intended to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral or with analytic functions of a complex variable. At the same time, he has included discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually will not find in books at this level.
This book is a carefully prepared account of the basic ideas inFourier analysis and its applications to the study of partialdifferential equations. The author succeeds to make his expositionaccessible to readers with a limited background, for example, thosenot acquainted with the Lebesgue integral. Readers should be familiarwith calculus, linear algebra, and complex numbers. A variety ofworked examples and exercises will help the readers to apply theirnewly acquired knowledge.
Introduction.- Preparations.- Laplace and Z Transforms.- Fourier Series.- L^2 Theory.- Separation of Variables.- Fourier Transforms.- Distributions.- Multi-Dimensional Fourier Analysis.- Appendix A: The ubiquitous convolution.- Appendix B: The Discrete Fourier Transform.- Appendix C: Formulae.- Appendix D: Answers to exercises.- Appendix E: Literature.