Advanced Engineering Mathematics with MATLAB (Hardcover, 4)

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

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