Advanced Engineering Mathematics with MATLAB®

1. INTRODUCTION Introduction to MATLAB(R) / MATLAB(R) Commands for Display and Plotting / Creating MATLAB(R) Programs / MATLAB(R) Programming Language / Problem Solving and Programming (Optional) / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 2. NUMBERS AND VECTORS Properties of Real Numbers / MATLAB(R) Computer Numbers (Optional) / Complex Numbers / Vectors in Two Dimensions and Three Dimensions / Vectors in Higher Dimensions / MATLAB(R) Vectors / Complex Vectors / Vector Spaces / Vector Spaces of Functions / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 3. MATRICES Basic Properties of Matrices / MATLAB(R) Matrix Operations / Square and Symmetric Matrices / Determinants and Matrix Inverses / Orthogonal and Triangular Matrices / Systems of Linear Equations / MATLAB(R) 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(R) 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(R) Solutions of Systems of Differential Equations / Homogeneous 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(R) 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(R) Commands for Discrete Systems / z-Transform Solution of Difference Equations / Applications of z-transforms to Linear Discrete Systems / Frequency Response and Fourier Analysis / Summary of z-transform Properties / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 11. THE DISCRETE FOURIER TRANSFORM AND THE FFT Frequency Analysis of Signals / Discrete and Fast Fourier Transforms / MATLAB(R) 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(R) Two-Dimensional Interpolation / MATLAB(R) 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(R) 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(R) 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 / INDEX / INDEX OF MATLAB(R) COMMANDS