Designed to give undergraduate engineering students a practical
and rigorous introduction to the fundamentals of
This book is a thoroughly modern
exposition of classic numerical methods using MATLAB. The fundamental
theory of each method is briefly developed. Rather than providing a
detailed numerical analysis, the behavior of the methods is exposed by
carefully designed numerical experiments. The methods are then
exercised on several nontrivial example problems from engineering
practice. The material in each chapter is organized as a progression
from the simple to the complex. This leads the student to an
understanding of the sophisticated numerical methods that are part of
MATLAB. An integral part of the book is the Numerical Methods with
MATLAB (NMM) Toolbox, which provides 150 programs and over forty data
sets. The NMM Toolbox is a library of numerical techniques implemented
in structured and clearly written code.
(NOTE: Chapters 2-12
conclude with Summary.)Terminology. MATLAB Overview. Organization of the Book.
Rating Systems for Exercises.
I. MATLAB BASICS.
2. Interactive Computing with MATLAB.
MATLAB. Matrices and Vectors. Additional Types of Variables. Managing
the Interactive Environment. Plotting in MATLAB.3. MATLAB
Script m-Files. Function m-Files. Input
and Output. Flow Control. Vectorization. Deus ex Machina.4.
Organizing and Debugging MATLAB Programs.
and Documenting m-Files. Organizing a Numerical Solution.
II. NUMERICAL TECHNIQUES. 5.
Unavoidable Errors in Computing.
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
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.
Ideas and Nomenclature. Newton-Cotes Rules. Gaussian Quadrature.
Adaptive Quadrature. Improper Integrals and Other
Complications.12. Numerical Integration of Ordinary
Basic Ideas and Nomenclature.
Euler's Method. Higher Order One-Step Methods. Adaptive Stepsize
Algorithms. Coupled ODEs. Additional
Appendix A: Eigenvalues and
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