Duffy Dean G. Advanced Engineering Mathematics: A Second Course with MatLAB

CRC Press, 2022. — 466 p. — ISBN 978-1032223452.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.DedicationAuthorList of DefinitionsComplex Variable
Complex Numbers
Finding Roots
The Derivative in the Complex Plane: The Cauchy-Riemann Equations Line Integrals
The Cauchy-Goursat Theorem
Cauchy’s Integral Formula
Taylor and Laurent Expansions and Singularities
Theory of Residues
Evaluation of Real Definite Integrals
Cauchy’s Principal Value Integral
Conformal MappingAdvanced Transform Methods
Inversion of Fourier Transforms by Contour Integration
Inversion of Laplace Transforms by Contour Integration
Integral Equations
The Solution of the Wave Equation by Using Laplace Transforms
The Solution of the Heat Equation by Using Laplace Transforms
The Solution of Laplace’s Equation by Using Laplace TransformsThe Z-Transform
The Relationship of the Z-Transform to the Laplace Transform
Some Useful Properties
Inverse Z-Transforms
Solution of Difference Equations
Stability of Discrete-Time SystemsThe Hilbert Transform
Definition
Some Useful Properties
Analytic Signals
Causality: The Kramers-Kronig RelationshipGreen’s Functions
What Is a Green’s Function?
Ordinary Differential Equations
Joint Transform Method
Wave Equation
Heat Equation
Helmholtz’s Equation
Galerkin MethodProbability
Review of Set Theory
Classic Probability
Discrete Random Variables
Continuous Random Variables
Mean and Variance
Some Commonly Used Distributions
Joint DistributionsRandom Processes
Fundamental Concepts
Power Spectrum
Two-State Markov Chains
Birth and Death Processes
Poisson ProcessesItô’s Stochastic Calculus
Random Differential Equations
Random Walk and Brownian Motion
Itô’s Stochastic Integral
Itô’s Lemma
Stochastic Differential Equations
Numerical Solution of Stochastic Differential Equations
Answers to the Odd-Numbered Problems