Norman John Richert, Ph.D., Claremont Graduate School
Summary
Advanced Engineering Mathematics using MATLAB® is written for engineers and engineering students who are
interested in applying MATLAB to solve practical engineering problems. The book emphasizes mathematical principles,
not computations, with MATLAB employed as a tool for analysis that shows how engineering problems are defined and
solved. The underlying philosophy of the book is: "The purpose of computing is insight, not numbers."
The book features complete MATLAB integration throughout, abundant examples that show real practical applications,
and end-of-chapter problems that reinforce techniques.
Table of Contents
1. INTRODUCTION.
Introduction to MATLAB®. MATLAB® Commands for Display and Plotting.
Creating MATLAB® Programs.
MATLAB® Programming Language.
Problem Solving and Programming (Optional).
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
2. NUMBERS AND VECTORS.
Properties of Real Numbers.
MATLAB® Computer Numbers (Optional).
Complex Numbers.
Vectors in Two Dimensions and Three Dimensions.
Vectors in Higher Dimensions.
MATLAB® Vectors.
Properties of Vectors.
Complex Vectors.
Vector Spaces.
Vector Spaces of Functions.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
3. MATRICES.
Basic Properties of Matrices.
MATLAB® Matrix Operations.
Square and Symmetric Matrices.
Determinants and Matrix Inverses.
Orthogonal and Triangular Matrices.
Systems of Linear Equations.
MATLAB® Matrix Functions.
Linear Transformations.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
4. EIGENVALUES AND EIGENVECTORS.
General Discussion of Eigenvalues.
Eigenvalues and Eigenvectors.
Matrix Eigenvalue Theorems.
Complex Vectors and Matrices.
MATLAB® Commands for Eigenvectors.
Matrix Calculus.
Similar and Diagonalizable Matrices.
Special Matrices and Their Eigenvalues (Optional).
Applications to Differential Equations.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
5. LINEAR DIFFERENTIAL EQUATIONS.
Classification of Differential Equations.
Linear Differential Equations.
Higher-Order Differential Equations.
Second-Order Differential Equations.
Particular Solutions of Differential Equations.
Systems of Differential Equations.
MATLAB® Solutions of Systems of Differential Equations.
Homogeneous Systems with Repeated Eigenvalues.
Nonhomogeneous Systems with Repeated Eigenvalues.
Nonhomogeneous Systems of Differential Equations.
Transforming Differential Equations.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
6. ADVANCED DIFFERENTIAL EQUATIONS.
Functions and Differential Equations.
Sequences and Series.
Taylor Series.
Numerical Methods for Differential Equations.
Stiff Differential Equations.
Vector Equations.
Boundary Value Problems.
Equations with Variable Coefficients.
Bessel and Legendre Equations.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
7. APPROXIMATION OF FUNCTIONS.
Polynomial Interpolation.
Interpolation by Spline Functions.
Least-Squares Curve Fitting.
Orthogonal Functions.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
8. FOURIER ANALYSIS.
Fourier Series.
Properties of Fourier Series.
Fourier Transforms.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
9. LAPLACE TRANSFORMS.
Definition and Properties of the Laplace Transform.
Computation of Inverse Laplace Transforms.
MATLAB® and Laplace Transforms.
Applications to Differential Equations.
Applications of Laplace Transforms to Linear Systems.
Relationship of Fourier and Laplace Transforms.
Summary of Laplace Transform Properties.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
10. DISCRETE SYSTEMS.
Introduction to the Sequences and Discrete Functions.
Linear Difference Equations.
Approximation to Differential Equations.
Smoothing and Digital Filters.
Introduction to Z-transforms.
MATLAB® Commands for Discrete Systems.
Z-Transform Solution of Difference Equations.
Applications of Z-transforms to Linear Discrete Systems.
Z-transforms and the Frequency Response.
Summary of Z-transform Properties.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
11. THE DISCRETE FOURIER TRANSFORM.
Frequency Analysis of Signals.
Discrete and Fast Fourier Transforms.
MATLAB® Fourier Commands.
Practical Signal Analysis.
Practical Signal Sampling and DFT Errors.
Analysis of DFT for Computation (Optional).
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
12. ADVANCED CALCULUS.
Functions of Several Variables.
Derivatives of a Multivariate Function.
Differentials and Linear Approximation.
Two-Dimensional Taylor Series.
MATLAB® Two-Dimensional Interpolation.
MATLAB® Differentiation.
Extrema of Real-Valued Functions.
Constrained Extrema and Lagrange Multipliers.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
13. VECTOR DIFFERENTIAL OPERATORS.
Vector and Scalar Fields.
MATLAB® Commands for Vector Differential Calculus.
Directional Derivatives and the Gradient.
The Divergence.
The Curl.
The Laplacian and Laplace's Equation.
Vector Field Theory.
Physical Application and Interpretation.
Curvilinear Coordinates.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
14. VECTOR INTEGRAL CALCULUS.
Integration.
Applications of Single Integrals.
Double and Triple Integrals.
Change of Variables in Double Integrals.
Change of Variables in Triple Integrals.
Applications of Multiple Integrals.
MATLAB® Commands for Integration.
Line Integrals.
Surface Integrals.
Theorems of Vector Integral Calculus.
Applications of Vector Field Theory.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
15. PARTIAL DIFFERENTIAL EQUATIONS.
Introduction to Partial Differential Equations.
Laplace's Equation.
The Heat Equation.
The Wave Equation.
Reinforcement Exercises and Exploration Problems.
Annotated Bibliography.
Answers.
