 4th Edition

# Advanced Engineering Mathematics with MATLAB

By

,

## Dean G. Duffy

ISBN 9781498739641
Published December 22, 2016 by Chapman and Hall/CRC
1004 Pages 104 Color & 239 B/W Illustrations

USD \$155.00

Prices & shipping based on shipping country

## Book Description

Advanced Engineering Mathematics with MATLAB, Fourth Edition builds upon three successful previous editions. It is written for today’s STEM (science, technology, engineering, and mathematics) student.

Three assumptions under lie its structure: (1) All students need a firm grasp of the traditional disciplines of ordinary and partial differential equations, vector calculus and linear algebra. (2) The modern student must have a strong foundation in transform methods because they provide the mathematical basis for electrical and communication studies. (3) The biological revolution requires an understanding of stochastic (random) processes. The chapter on Complex Variables, positioned as the first chapter in previous editions, is now moved to Chapter 10.

The author employs MATLAB to reinforce concepts and solve problems that require heavy computation. Along with several updates and changes from the third edition, the text continues to evolve to meet the needs of today’s instructors and students.

Features:

• Complex Variables, formerly Chapter 1, is now Chapter 10.
• A new Chapter 18: Itô’s Stochastic Calculus.
• Implements numerical methods using MATLAB, updated and expanded
• Takes into account the increasing use of probabilistic methods in engineering and the physical sciences
• Includes many updated examples, exercises, and projects drawn from the scientific and engineering literature
• Draws on the author’s many years of experience as a practitioner and instructor
• Gives answers to odd-numbered problems in the back of the book

CLASSIC ENGINEERING MATHEMATICS

First-Order Ordinary Differential Equations
Classification of Differential Equations
Separation of Variables
Homogeneous Equations
Exact Equations
Linear Equations
Graphical Solutions
Numerical Methods

Higher-Order Ordinary Differential Equations
Homogeneous Linear Equations with Constant Coefficients
Simple Harmonic Motion
Damped Harmonic Motion
Method of Undetermined Coefficients
Forced Harmonic Motion
Variation of Parameters
Euler-Cauchy Equation
Phase Diagrams
Numerical Methods

Linear Algebra
Fundamentals of Linear Algebra
Determinants
Cramer’s Rule
Row Echelon Form and Gaussian Elimination
Eigenvalues and Eigenvectors
Systems of Linear Differential Equations
Matrix Exponential

Vector Calculus
Review
Divergence and Curl
Line Integrals
The Potential Function
Surface Integrals
Green’s Lemma
Stokes’ Theorem
Divergence Theorem

Fourier Series
Fourier Series
Properties of Fourier Series
Half-Range Expansions
Fourier Series with Phase Angles
Complex Fourier Series
The Use of Fourier Series in the Solution of Ordinary Differential Equations
Finite Fourier Series

The Sturm-Liouville Problem
Eigenvalues and Eigenfunctions
Orthogonality of Eigenfunctions
Expansion in Series of Eigenfunctions
A Singular Sturm-Liouville Problem: Legendre’s Equation
Another Singular Sturm-Liouville Problem: Bessel’s Equation
Finite Element Method

The Wave Equation
The Vibrating String
Initial Conditions: Cauchy Problem
Separation of Variables
D’Alembert’s Formula
Numerical Solution of the Wave Equation

The Heat Equation
Derivation of the Heat Equation
Initial and Boundary Conditions
Separation of Variables
Numerical Solution of the Heat Equation

Laplace’s Equation
Derivation of Laplace’s Equation
Boundary Conditions
Separation of Variables
Poisson’s Equation on a Rectangle
Numerical Solution of Laplace’s Equation
Finite Element Solution of Laplace’s Equation

TRANSFORM METHODS

Complex Variables
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 Mapping

The Fourier Transform
Fourier Transforms
Fourier Transforms Containing the Delta Function
Properties of Fourier Transforms
Inversion of Fourier Transforms
Convolution
Solution of Ordinary Differential Equations
The Solution of Laplace’s Equation on the Upper Half-Plane
The Solution of the Heat Equation

The Laplace Transform
Definition and Elementary Properties
The Heaviside Step and Dirac Delta Functions
Some Useful Theorems
The Laplace Transform of a Periodic Function
Inversion by Partial Fractions: Heaviside’s Expansion Theorem
Convolution
Integral Equations
Solution of Linear Differential Equations with Constant Coefficients
Inversion by Contour Integration
The Solution of the Wave Equation
The Solution of the Heat Equation
The Superposition Integral and the Heat Equation
The Solution of Laplace’s Equation

The 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 Systems

The Hilbert Transform
Definition
Some Useful Properties
Analytic Signals
Causality: The Kramers-Kronig Relationship

Green’s Functions
What Is a Green’s Function?
Ordinary Differential Equations
Joint Transform Method
Wave Equation
Heat Equation
Helmholtz’s Equation
Galerkin Methods

STOCHASTIC PROCESSES

Probability
Review of Set Theory
Classic Probability
Discrete Random Variables
Continuous Random Variables
Mean and Variance
Some Commonly Used Distributions
Joint Distributions

Random Processes
Fundamental Concepts
Power Spectrum
Two-State Markov Chains
Birth and Death Processes
Poisson Processes

Itˆo’s Stochastic Calculus
Random Differential Equations
Random Walk and Brownian Motion
Itˆo’s Stochastic Integral
Itˆo’s Lemma
Stochastic Differential Equations
Numerical Solution of Stochastic Differential Equations

...

## Author(s)

### Biography

Dean G. Duffy is a former mathematics instructor at the US Naval Academy and US Military Academy. He spent 25 years working on numerical weather prediction, oceanic wave modeling, and dynamical meteorology at NASA’s Goddard Space Flight Center. Prior to this, he was a numerical weather prediction officer in the US Air Force. He earned his Ph.D. in meteorology from MIT. Dr. Duffy has written several books on transform methods, engineering mathematics, Green’s functions, and mixed boundary value problems.

## Support Material

### Ancillaries

• Instructor Resources