Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. NUMERICAL MATHEMATICS AND COMPUTING, 7th Edition also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors.
Some sections and material have been re-moved from the new edition such as the introductory section on numerical integration. Some material and many bibliographical items have been moved from the textbook to the website.
The first two chapters in the previous edition on Mathematical Preliminaries, Taylor Series, Oating-Point Representation, and Errors have been combined into a single introductory chapter to allow instructors and students to move quickly.
The two chapters, in the previous edition, on Ordinary Differential Equations have been combined into one chapter.
NEW! Exercises, computer exercises, and application exercises have been added to the text.
NEW! A section of Fourier Series and Fast Fourier Transforms has been added.
UPDATED! The Solving Systems of Linear Equations chapter has been moved earlier in the text to provide more clarity throughout the text.
Appendices: Reorganized and revamped, new appendices offer a wealth of supplemental material, including advice on good programming practices, coverage of numbers in different bases, details on IEEE floating-point arithmetic, and discussions of linear algebra concepts and notation.
Visual Learning: Because concrete codes and visual aids are helpful to every reader, the authors have added even more figures and numerical examples throughout the text--ensuring students gain solid understanding before advancing to new topics.
Comprehensive, Current and Cutting Edge: Completely updated, the new edition includes new sections and material on such topics as the modified false position method, the conjugate gradient method, Simpsons method, and more.
More Accessible: Computer codes and other material are now included on the text website--giving you and your students easy access without tedious typing. Matlab, Mathematica, and Maple computer codes and the Overview of Mathematical Software appendix are all now available online.
Hands-On Applications: Giving students myriad opportunities to put chapter concepts into real practice, additional exercises involving applications are presented throughout.
References: Citation to recent references reflects the latest developments from the field.
Table of Contents
1. MATHEMATICAL PRELIMINARIES AND FLOATING-POINT REPRESENTATION.
2. LINEAR SYSTEMS.
3. NONLINEAR EQUATIONS.
4. INTERPOLATION AND NUMBERICAL DIFFERENTIATION.
5. NUMERICAL INTEGRATION.
6. SPLINE FUNCTIONS.
7. INITIAL VALUES PROBLEMS.
8. MORE ON LINEAR SYSTEMS.
9. LEAST SQUARES METHODS AND FOURIER SERIES.
10. MONTE CARLO METHODS AND SIMULATION.
11. BOUNDARY-VALUE PROBLEMS.
12. PARTIAL DIFFERENTIAL EQUATIONS.
13. MINIMIZATION OF FUNTIONS.
14. LINEAR PROGRAMMING PROBLEMS.
APPENDIX A. ADVICE ON GOOD PROGRAMMING PRACTICES.
APPENDIX B. REPRESENTATION OF NUMBERS IN DIFFERENT BASES.
APPENDIX C. ADDITIONAL DETAILS ON IEEE FLOATING-POINT ARITHMETIC.
APPENDIX D. LINEAR ALGEBRA CONCEPTS AND NOTATION.
Ward Cheney is Professor of Mathematics at the University of Texas at Austin. His research interests include approximation theory, numerical analysis, and extremum problems.
David Kincaid is Senior Lecturer in the Department of Computer Sciences at the University of Texas at Austin. Also, he is the Interim Director of the Center for Numerical Analysis (CNA) within the Institute for Computational Engineering and Sciences (ICES).