Content: Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Acknowledgments
Author
Introduction
List of Definitions
CLASSIC ENGINEERING MATHEMATICS
Chapter 1: First-Order Ordinary Differential Equations
1.1 Classification of Differential Equations
1.2 Separation of Variables
1.3 Homogeneous Equations
1.4 Exact Equations
1.5 Linear Equations
1.6 Graphical Solutions
1.7 Numerical Methods
Chapter 2: Higher-Order Ordinary Differential Equations
2.1 Homogeneous Linear Equations with Constant Coefficients
2.2 Simple Harmonic Motion
2.3 Damped Harmonic Motion. 2.4 Method of Undetermined Coefficients2.5 Forced Harmonic Motion
2.6 Variation of Parameters
2.7 Euler-Cauchy Equation
2.8 Phase Diagrams
2.9 Numerical Methods
Chapter 3: Linear Algebra
3.1 Fundamentals of Linear Algebra
3.2 Determinants
3.3 Cramer's Rule
3.4 Row Echelon Form and Gaussian Elimination
3.5 Eigenvalues and Eigenvectors
3.6 Systems of Linear Differential Equations
3.7 Matrix Exponential
Chapter 4: Vector Calculus
4.1 Review
4.2 Divergence and Curl
4.3 Line Integrals
4.4 The Potential Function
4.5 Surface Integrals
4.6 Green's Lemma
4.7 Stokes' Theorem. 4.8 Divergence TheoremChapter 5: Fourier Series
5.1 Fourier Series
5.2 Properties of Fourier Series
5.3 Half-Range Expansions
5.4 Fourier Series with Phase Angles
5.5 Complex Fourier Series
5.6 The Use of Fourier Series in the Solution of Ordinary Differential Equations
5.7 Finite Fourier Series
Chapter 6: The Sturm-Liouville Problem
6.1 Eigenvalues and Eigenfunctions
6.2 Orthogonality of Eigenfunctions
6.3 Expansion in Series of Eigenfunctions
6.4 A Singular Sturm-Liouville Problem: Legendre's Equation
6.5 Another Singular Sturm-Liouville Problem: Bessel's Equation. 6.6 Finite Element MethodChapter 7: The Wave Equation
7.1 The Vibrating String
7.2 Initial Conditions: Cauchy Problem
7.3 Separation of Variables
7.4 D'Alembert's Formula
7.5 Numerical Solution of the Wave Equation
Chapter 8: The Heat Equation
8.1 Derivation of the Heat Equation
8.2 Initial and Boundary Conditions
8.3 Separation of Variables
8.4 Numerical Solution of the Heat Equation
Chapter 9: Laplace's Equation
9.1 Derivation of Laplace's Equation
9.2 Boundary Conditions
9.3 Separation of Variables
9.4 Poisson's Equation on a Rectangle. 9.5 Numerical Solution of Laplace's Equation9.6 Finite Element Solution of Laplace's Equation
TRANSFORM METHODS
Chapter 10: Complex Variables
10.1 Complex Numbers
10.2 Finding Roots
10.3 The Derivative in the Complex Plane: The Cauchy-Riemann Equations
10.4 Line Integrals
10.5 The Cauchy-Goursat Theorem
10.6 Cauchy's Integral Formula
10.7 Taylor and Laurent Expansions and Singularities
10.8 Theory of Residues
10.9 Evaluation of Real Definite Integrals
10.10 Cauchy's Principal Value Integral
10.11 Conformal Mapping
Chapter 11: The Fourier Transform
11.1 Fourier Transforms.