Unique in content and approach, this book covers all the topics that are usually covered in an introduction to scientific computing--but folds in graphics and matrix-vector manipulation in a way that gets readers to appreciate theconnection between continuous mathematics and computing. MATLAB 5 is usedthroughout to encourage experimentation, and each chapter focuses on a different important theorem--allowing readers to appreciate the rigorous side of scientific computing. In addition to standard topical coverage, each chapter includes 1) a sketch of a “hard” problem that involves ill-conditioning, high dimension, etc.; 2)at least one theorem with both a rigorous proof and a “proof by MATLAB” experiment to bolster intuition; 3)at least one recursive algorithm; and 4)at least one connection to a real-world application. The book revolves around examples that are packaged in 200+ M-files, which, collectively, communicate all the key mathematical ideas and an appreciation for the subtleties of numerical computing.Power Tools of the Trade. Polynomial Interpolation. Piecewise Polynomial Interpolation. Numerical Integration. Matrix Computations. Linear Systems. The QR and Cholesky Factorizations. Nonlinear Equations and Optimization. The Initial Value Problem.For engineers and mathematicians.
Unique in content and approach, this piece covers all the topics that are usually covered in an introduction to scientific computingbut folds in graphics and matrix-vector manipulation in a way that gets readers to appreciate the connection between continuous mathematics and computing. Matlab 5 is used throughout to encourage experimentation, and each chapter focuses on a different important theoremallowing users to appreciate the rigorous side of scientific computing. In addition to standard topical coverage, each chapter includes 1) a sketch of a "hard" problem that involves ill-conditioning, high dimension, etc.; 2) at least one theorem with both a rigorous proof and a "proof by MATLAB" experiment to bolster intuition; 3) at least one recursive algorithm; and 4) at least one connection to a real-world application.
FEATURES/BENEFITS
- NEWUpgraded to a MATLAB 5 level.
- NEWApproximately 60 new problems.,
- NEWNew sections on structure arrays, cell arrays, and how to produce more informative plots (Ch. 1).
- NEWA brief treatment of trigonometric interpolation (Ch. 2)A follow-up FFT solution to the problem is provided in Ch. 5).
- NEWA brief discussion of sparse arrays (Ch. 5).
- Permits a limited study of sparse methods for linear equations and least squares in Chs. 6 and 7.
- NEWBlock matrix materialNow enriched with the use of cell arrays (Chs. 6-7).
- NEWOrbit problem solutionsNow make use of simple structures (Ch. 8).
- Simplifies the presentation.
- NEWMore detailed coverage of "ode23" (Ch. 9).
- NEWWebsiteProvides solutions to half the problems.
- Additional coverage of graphics.
- Numerical linear algebraPermeates the entire presentation, beginning in Ch. 1. (This is a get-started-with-MATLAB tutorial, but is driven by examples that set the stage for the numerical algorithms that follow.)
- One important theorem covered per chapter.
- Motivational examples and related homework problems using MATLAB.
- Allows users to get a personal feel for algorithm strengths and weaknesses without the distraction of debugging the syntax of a compiled higher level language.
- An abundance of examples, packaged in 200+ M-filesThe book revolves around examples that are packaged in 200+ M-files, which, collectively, communicate all the key mathematical ideas and an appreciation for the subtleties of numerical computing.
- Snapshots of advanced computingIn sections that deal with parallel adaptive quadrature and parallel matrix computations. Treatment of recursion includes divided differences, adaptive approximation, quadrature, the fast Fourier transform, Strassen matrix multiplication, and the Cholesky factorization.
