This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science.
Author(s): R. J. Beerends, H. G. Ter Morsche, J. C. Van den Berg, E. M. Van de Vrie
Publisher: Cambridge University Press
Year: 2003
Language: English
Pages: 459
City: Leiden
Tags: Математика;Операционное исчисление;
Content: Cover; Half-title; Title; Copyright; Contents; Preface; Introduction; Part 1 Applications and foundations; CHAPTER 1 Signals and systems; CHAPTER 2 Mathematical prerequisites; Part 2 Fourier series; INTRODUCTION TO PART 2; CHAPTER 3 Fourier series: definition and properties; CHAPTER 4 The fundamental theorem of Fourier series; CHAPTER 5 Applications of Fourier series; Part 3 Fourier integrals and distributions; INTRODUCTION TO PART 3; CHAPTER 6 Fourier integrals: definition and properties; CHAPTER 7 The fundamental theorem of the Fourier integral; CHAPTER 8 Distributions. CHAPTER 9 The Fourier transform of distributionsCHAPTER 10 Applications of the Fourier integral; Part 4 Laplace transforms; INTRODUCTION TO PART 4; CHAPTER 11 Complex functions; CHAPTER 12 The Laplace transform: definition and properties; CHAPTER 13 Further properties, distributions, and the fundamental theorem; CHAPTER 14 Applications of the Laplace transform; Part 5 Discrete transforms; INTRODUCTION TO PART 5; CHAPTER 15 Sampling of continuou.
Abstract: Textbook on Fourier and Laplace transforms for undergraduate and graduate students
