Elementary Numerical Analysis, 3rd Edition
October 2003, ©2004
Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems.
The text introduces core areas of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic.
Chapter 2. Error and Computer Arithmetic.
Chapter 3. Rootfinding.
Chapter 4. Interpolation and Approximation.
Chapter 5. Numerical Integration and Differentiation.
Chapter 6. Solution of Systems of Linear Equations.
Chapter 7. Numerical Linear Algebra: Advanced Topics.
Chapter 8. Ordinary Differential Equations.
Chapter 9. Finite Difference Method for PDEs.
Appendix A: Mean Value Theorems.
Appendix B: Mathematical Formulas.
Appendix C: Numerical Analysis Software Packages.
Appendix D: Matlab: An Introduction.
Appendix E: The Binary Number System.
Answers to Selected Problems.
- New Chapter 9 on numerical methods for the classic second order linear partial differential equations in two variables.
- New Section 4.7 on least squares approximation of functions, including an introduction to Legendre polynomials.
- New Section 8.8 on the two-point boundary value problem.
- A rewritten section on computer arithmetic now concentrates on the IEEE floating-point format for representing numbers in computers.
- Programming language changed from Fortran to MATLAB.
- From the text's Web site at www.wiley.com/college/atkinson, instructors and students will have access to online resources: Overhead slides, MATLAB Programs, Numerical Examples, and MATLAB Programs with a Graphical User Interface.
- Flexible: The text offers comprehensive coverage of virtually all major topics in numerical analysis. Its flexible Table of Contents allows instructors to choose exactly what material to cover in a one-semester course.
- Varied end-of-chapter exercises: Some exercises provide additional illustrations of the theoretical results given in the section, and a number of these exercises can be done with either a hand calculator or with a simple computer program.
- MATLAB Programs: For a number of exercises, students are asked to modify the programs in order to solve specific problems. This approach enables students to learn programming more efficiently, and allows them to focus more on technique learning and problem solving.
- Appropriate level: The mathematical treatment of the material is kept at a manageable level--not too deep, not too elementary. It can be used with students who have had a one-year course in single-variable calculus, although some background in linear algebra and differential equations is helpful for chapters 6-9.
--Barbara Shabell, California State Polytechnic University, Pomona
“There is a right kind of mix of theory and exercises and the order in which the topics have been presented is appropriate for my taste in teaching undergraduate students.”
--Prabir Daripa, Texas A&M University
“I find this book to be a pleasure to read; it is filled with mathematical insight into numerical analysis at a level appropriate for undergraduates. The clarity of exposition is one of the strongest assets of this book.”
--David J. Horntrop, New Jersey Institute of Technology
“The writing style of this book is precise and easy to understand. We particularly appreciate the format that to illustrate an approach, a simple numerical example is presented first. This format is used consistently throughout the text. Compared to our current text, this new text explains ideas in more straightforward and crystal-clear ways. It will be quite easy for students to use and learn the basic ideas. I think I would prefer this text to our current text for presentations of the materials.”
--Jingyi Zhu, University of Utah