دانلود کتاب تجزیه و تحلیل فوریه و توزیع

Fourier analysis and distribution theory are fundamental mathematical tools for describing and solving a wide array of technical and scientific problems. These include areas of physics, mechanical engineering, electrical engineering, and signal and control theory. This text is intended for future scientists seeking to understand the theoretical foundation of mathematical modeling, Fourier analysis methods, and their practical applications. It builds on the author’s earlier work, published by Vieweg in 1996, and incorporates insights from many years of lectures delivered to students of applied mathematics, physics, electrical engineering, and communications engineering at the Technische Hochschule Nürnberg Georg Simon Ohm, starting in their fourth semester. The book is tailored for undergraduate and early master’s students in mathematics, physics, and engineering. A basic understanding of differential and integral calculus is a prerequisite. The text is divided into chapters covering the mathematical foundations of Fourier series, distributions, and Fourier transforms, each complemented by examples of practical applications. The fundamentals of distribution theory, widely used in engineering disciplines, enable and simplify numerous calculations for physical and technical problems. The book is structured such that theoretical and application-oriented chapters each account for half of the content. The theoretical chapters introduce Fourier series and integrals, distributions, and the z-Transform. The application chapters are designed to be read independently, depending on the reader’s interest. These chapters provide an introduction to the fundamental types of linear partial differential equations and essential principles of linear systems theory. Topics include methods for linear filter design and sampling, offering an accessible introduction to modern signal processing. The unified representation of analog and discrete linear systems within the framework of distributions is also explored. The sections on discrete Fourier and wavelet transforms, along with their applications in signal processing, and the introductory discussion on the finite element method, provide a glimpse into the numerical aspects of practical applications. Specific examples utilize physical SI units to ground the concepts in real-world scenarios. Through this book, I aim to offer mathematics and physics students a clear introduction to widely used techniques in technology and engineering. Simultaneously, I hope to provide technically oriented students with a comprehensible mathematical presentation that supports their work. To facilitate learning, the text includes 175 illustrations. I trust that the presentation will encourage readers to apply their newly acquired knowledge in practice and continue their learning journey with other available literature if necessary. The appendices include essential theorems from function theory and Lebesgue integration, which are used throughout the text. I would like to express my gratitude to my colleagues Herbert Leinfelder, Rudolf Rupp, and Jörg Steinbach in Nürnberg, and Peter Wagner in Innsbruck, for their valuable discussions during the preparation of this book. Special thanks go to Donna Chernyk and Kirithiga Nandini Gnanasekaran at Springer Nature for their professional assistance in publishing this text. I am also indebted to Charlott Caroline, Krefeld, and Friederike Laus, Niederzissen, for translating and typesetting several chapters from German into English, and to my students, whose motivated collaboration and constructive feedback in lectures and seminars contributed significantly to the development of this book. An important part of this book are the exercises, which I encourage serious readers to complete independently. Most exercises are designed to reinforce the content of the book and develop strong calculation techniques. Exercises marked with an asterisk are primarily intended for mathematicians and sometimes explore topics not discussed in detail within the text. For reference, solutions to all exercises are provided in Appendix C.