## Table of Contents

(NOTE: Chapters 2-12 conclude with Summary.)

**1. Introduction.**

Terminology. MATLAB Overview. Organization of the Book. Rating Systems for Exercises.

**I. MATLAB BASICS.**

**2. Interactive Computing with MATLAB.**

Running MATLAB. Matrices and Vectors. Additional Types of Variables. Managing the Interactive Environment. Plotting in MATLAB.

**3. MATLAB Programming.**

Script m-Files. Function m-Files. Input and Output. Flow Control. Vectorization. Deus ex Machina.

**4. Organizing and Debugging MATLAB Programs.**

Organizing and Documenting m-Files. Organizing a Numerical Solution. Debugging.

**II. NUMERICAL TECHNIQUES.**

**5. Unavoidable Errors in Computing.**

Digital Representation of Numbers. Finite Precision Arithmetic. Truncation Error of Algorithms.

**6. Finding the Roots of f(x)=0.**

Preliminaries. Fixed-Point Iteration. Bisection. Newton's Method. The Secant Method. Hybrid Methods. Roots of Polynomials.

**7. A Review of Linear Algebra.**

Vectors. Matrices. Mathematical Properties of Vectors and Matrices. Special Matrices.

**8. Solving Systems of Equations.**

Basic Concepts. Gaussian Elimination. Limitations on Numerical Solutions to Ax = b. Factorization Methods. Nonlinear Systems of Equations.

**9. Least-Squares Fitting of a Curve to Data.**

Fitting a Line to Data. Least-Squares Fit to a Linear Combination of Functions. Multivariate Linear Least-Squares Fitting.

**10. Interpolation.**

Basic Ideas. Interpolating Polynomials of Arbitrary Degree. Piecewise Polynomial Interpolation. MATLAB's Built in Interpolation Functions.

**11. Numerical Integration.**

Basic Ideas and Nomenclature. Newton-Cotes Rules. Gaussian Quadrature. Adaptive Quadrature. Improper Integrals and Other Complications.

**12. Numerical Integration of Ordinary Differential Equations.**

Basic Ideas and Nomenclature. Euler's Method. Higher Order One-Step Methods. Adaptive Stepsize Algorithms. Coupled ODEs. Additional Topics.

**Bibliography.**

**Appendix A: Eigenvalues and Eigensystems.**

Eigenvectors Map onto Themselves. Mathematical Preliminaries. The Power Method. Built-in Functions for Eigenvalue Computation. Singular Value Decomposition.

**Appendix B: Sparse Matrices.**

Storage and Flop Savings. MATLAB Sparse Matrix Format.

**MATLAB Toolbox Functions.**

**Listings for NMM Toolbox m-Files.**

**Subject Index.**

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