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Other titles in the Featured Titles for Numerical Analysis series:Introduction to Numerical Methods and MATLAB: Implementations and Applicationsby Gerald W. Reckenwald
Synopses & ReviewsPublisher Comments:This book is an introduction to MATLAB and an introduction to numerical methods. It is written for students of engineering, applied mathematics, and science. The primary objective of numerical methods is to obtain approximate solutions to problems that are not obtainable by other means. This book teaches how the core techniques of numerical methods are used to solve otherwise unsolvable problems of modern technological significance.
The outstanding pedagogical features of this book are:
The primary goals of the book are to provide a solid foundation in applied computing, and to demonstrate the implementation and application of standard numerical methods to practical problems. This is achieved by a systematic development of techniques beginning with the simple and ending with the sophisticated. Good programming practice is used throughout to show the reader how to clearly express and document computational ideas. By providing an extensive library of working codes, as well as an exposition of the methods used by the builtin MATLAB toolbox, the reader is challenged by the application of numerical methods to practical problems. This bypasses the ritual of forcing the reader to reinvent simple programs that fail on more technologically significant, practical problems. Synopsis:This thorough, modern exposition of classic numerical methods using MATLAB briefly develops the fundamental theory of each method. 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. This structured, concise, and efficient book contains a large number of examples of two basic typesOne type of example demonstrates a principle or numerical method in the simplest possible terms. Another type of example demonstrates how a particular method can be used to solve a more complex practical problem. The material in each chapter is organized as a progression from the simple to the complex. Contains an extensive reference to using MATLAB. This includes interactive (command line) use of MATLAB, MATLAB programming, plotting, file input and output. For a practical and rigorous introduction to the fundamentals of numerical computation.
Synopsis: This thorough, modern exposition of classic numerical methods using MATLAB briefly develops the fundamental theory of each method. 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. This structured, concise, and efficient book contains a large number of examples of two basic types—One type of example demonstrates a principle or numerical method in the simplest possible terms. Another type of example demonstrates how a particular method can be used to solve a more complex practical problem. The material in each chapter is organized as a progression from the simple to the complex. Contains an extensive reference to using MATLAB. This includes interactive (command line) use of MATLAB, MATLAB programming, plotting, file input and output. For a practical and rigorous introduction to the fundamentals of numerical computation.
About the AuthorGERALD RECKTENWALD is an Associate Professor of Mechanical Engineering at Portland State University, and regularly teaches courses in Numerical Methods.
Table of Contents(NOTE: Chapters 212 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 mFiles. Function mFiles. Input and Output. Flow Control. Vectorization. Deus ex Machina. 4. Organizing and Debugging MATLAB Programs.
Organizing and Documenting mFiles. 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. FixedPoint 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. LeastSquares Fitting of a Curve to Data.
Fitting a Line to Data. LeastSquares Fit to a Linear Combination of Functions. Multivariate Linear LeastSquares 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. NewtonCotes 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 OneStep Methods. Adaptive Stepsize Algorithms. Coupled ODEs. Additional Topics. Bibliography.
Appendix A: Eigenvalues and Eigensystems.
Eigenvectors Map onto Themselves. Mathematical Preliminaries. The Power Method. Builtin 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 mFiles.
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