Advanced Engineering Mathematics with MATLAB
Preview
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:
Table of Contents
CLASSIC ENGINEERING MATHEMATICS
FirstOrder Ordinary Differential Equations
Classification of Differential Equations
Separation of Variables
Homogeneous Equations
Exact Equations
Linear Equations
Graphical Solutions
Numerical Methods
HigherOrder 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
EulerCauchy 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
HalfRange 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 SturmLiouville Problem
Eigenvalues and Eigenfunctions
Orthogonality of Eigenfunctions
Expansion in Series of Eigenfunctions
A Singular SturmLiouville Problem: Legendre’s Equation
Another Singular SturmLiouville 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 CauchyRiemann Equations
Line Integrals
The CauchyGoursat 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 HalfPlane
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 ZTransform
The Relationship of the ZTransform to the Laplace Transform
Some Useful Properties
Inverse ZTransforms
Solution of Difference Equations
Stability of DiscreteTime Systems
The Hilbert Transform
Definition
Some Useful Properties
Analytic Signals
Causality: The KramersKronig 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
TwoState 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
To gain access to the instructor resources for this title, please visit the Instructor Resources Download Hub.
You will be prompted to fill out a registration form whic