Heath 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems. Changes for the second edition include: expanded motivational discussions and examples; formal statements of all major algorithms; expanded discussions of existence, uniqueness, and conditioning for each type of problem so that students can recognize "good" and "bad" problem formulations and understand the corresponding quality of results produced; and expanded coverage of several topics, particularly eigenvalues and constrained optimization. The book contains a wealth of material and can be used in a variety of one- or two-term courses in computer science, mathematics, or engineering. Its comprehensiveness and modern perspective, as well as the software pointers provided, also make it a highly useful reference for practicing professionals who need to solve computational problems.
Practical techniques for problem solving are emphasized over formal analysis, allowing the student to develop skills for handling real-world situations.
Applications are shown for the most popular computational software, including MATLAB, IMSL, and NAG.
Motivating examples are found throughout.
An abundance of graphical illustrations provides visual reinforcement for new concepts.
Appendices contain useful background information and references about where to find additional instructive resources.
Scalers, vectors, and matrices are each shown in a different font to assist beginners in distinguishing between them.
Table of Contents
1 Scientific Computing
2 Systems of Linear Equations
3 Linear Least Squares
4 Eigenvalues Problems
5 Nonlinear Equations
8 Numerical Integration and Differentiation
9 Initial Value Problems for ODEs
10 Boundary Value Problems for ODEs
11 Partial Differential Equations
12 Fast Fourier Transform
13 Random Numbers and Simulation