Through four previous editions of Advanced Engineering Mathematics with MATLAB, the author presented a wide variety of topics needed by today's engineers. The fifth edition of that book, available now, has been broken into two parts: topics currently needed in mathematics courses and a new stand-alone volume presenting topics not often included in these courses and consequently unknown to engineering students and many professionals.
The overall structure of this new book consists of two parts: transform methods and random processes. Built upon a foundation of applied complex variables, the first part covers advanced transform methods, as well as z-transforms and Hilbert transforms--transforms of particular interest to systems, communication, and electrical engineers. This portion concludes with Green's function, a powerful method of analyzing systems.
The second portion presents random processes--processes that more accurately model physical and biological engineering. Of particular interest is the inclusion of stochastic calculus.
The author continues to offer a wealth of examples and applications from the scientific and engineering literature, a highlight of his previous books. As before, theory is presented first, then examples, and then drill problems. Answers are given in the back of the book.
This book is all about the future: The purpose of this book is not only to educate the present generation of engineers but also the next.
The main strength is the text is written from an engineering perspective. The majority of my students are engineers. The physical examples are related to problems of interest to the engineering students. --Lea Jenkins, Clemson University
Author(s): Dean G. Duffy
Series: Advances in Applied Mathematics
Publisher: CRC Press
Year: 2022
Language: English
Pages: 448
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Acknowledgments
Author
Introduction
List of Definitions
Chapter 1: Complex Variables
1.1 Complex Numbers
1.2 Finding Roots
1.3 The Derivative in the Complex Plane: The Cauchy-Riemann Equations
1.4 Line Integrals
1.5 The Cauchy-Goursat Theorem
1.6 Cauchy’s Integral Formula
1.7 Taylor and Laurent Expansions and Singularities
1.8 Theory of Residues
1.9 Evaluation of Real Definite Integrals
1.10 Cauchy’s Principal Value Integral
1.11 Conformal Mapping
Chapter 2: Advanced Transform Methods
2.1 Inversion of Fourier Transforms by Contour Integration
2.2 Inversion of Laplace Transforms by Contour Integration
2.3 Integral Equations
2.4 The Solution of the Wave Equation by Using Laplace Transforms
2.5 The Solution of the Heat Equation by Using Laplace Transforms
2.6 The Solution of Laplace’s Equation by Using Laplace Transforms
Chapter 3: The Z-Transform
3.1 The Relationship of the Z-Transform to the Laplace Transform
3.2 Some Useful Properties
3.3 Inverse Z-Transforms
3.4 Solution of Difference Equations
3.5 Stability of Discrete-Time Systems
Chapter 4: The Hilbert Transform
4.1 Definition
4.2 Some Useful Properties
4.3 Analytic Signals
4.4 Causality: The Kramers-Kronig Relationship
Chapter 5: Green’s Functions
5.1 What Is a Green’s Function?
5.2 Ordinary Differential Equations
5.3 Joint Transform Method
5.4 Wave Equation
5.5 Heat Equation
5.6 Helmholtz’s Equation
5.7 Galerkin Method
Chapter 6: Probability
6.1 Review of Set Theory
6.2 Classic Probability
6.3 Discrete Random Variables
6.4 Continuous Random Variables
6.5 Mean and Variance
6.6 Some Commonly Used Distributions
6.7 Joint Distributions
Chapter 7: Random Processes
7.1 Fundamental Concepts
7.2 Power Spectrum
7.3 Two-State Markov Chains
7.4 Birth and Death Processes
7.5 Poisson Processes
Chapter 8: Itô’s Stochastic Calculus
8.1 Random Differential Equations
8.2 Random Walk and Brownian Motion
8.3 Itô’s Stochastic Integral
8.4 Itô’s Lemma
8.5 Stochastic Differential Equations
8.6 Numerical Solution of Stochastic Differential Equations
Answers to the Odd-Numbered Problems
Index
