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Numerical Mathematics and Computing (International Edition) Paperback – 8 May 2012


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1. INTRODUCTION. Preliminary Remarks. Review of Taylor Series. 2. FLOATING-POINT REPRESENTATION AND ERRORS. Floating-Point Representation. Loss of Significance. 3. LOCATING ROOTS OF EQUATIONS. Bisection Method. Newton's Method. Secant Method. 4. INTERPOLATION AND NUMERICAL DIFFERENTIATION. Polynomial Interpolation. Errors in Polynomial Interpolation. Estimating Derivatives and Richardson Extrapolation. 5. NUMERICAL INTEGRATION. Lower and Upper Sums. Trapezoid Rule. Romberg Algorithm. 6. ADDITIONAL TOPICS ON NUMERICAL INTEGRATION. Simpson's Rule and Adaptive Simpson's Rule. Gaussian Quadrature Formulas. 7. SYSTEMS OF LINEAR EQUATIONS. Naive Gaussian Elimination. Gaussian Elimination with Scaled Partial Pivoting. Tridiagonal and Banded Systems. 8. ADDITIONAL TOPICS CONCERNING SYSTEMS OF LINEAR EQUATIONS. Matrix Factorizations. Iterative Solutions of Linear Systems. Eigenvalues and Eigenvectors. Power Method. 9. APPROXIMATION BY SPLINE FUNCTIONS. First-Degree and Second-Degree Splines. Natural Cubic Splines. B Splines: Interpolation and Approximation. 10. ORDINARY DIFFERENTIAL EQUATIONS. Taylor Series Methods. Runge-Kutta Methods. Stability and Adaptive Runge-Kutta and Multistep Methods. 11. SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. Methods for First-Order Systems. Higher-Order Equations and Systems. Adams-Bashforth-Moulton Methods. 12. SMOOTHING OF DATA AND THE METHOD OF LEAST SQUARES. Method of Least Squares. Orthogonal Systems and Chebyshev Polynomials. Other Examples of the Least-Squares Principle. 13. MONTE CARLO METHODS AND SIMULATION. Random Numbers. Estimation of Areas and Volumes by Monte Carlo Techniques. Simulation. 14. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. Shooting Method Shooting Method Algorithm. A Discretization Method. 15. PARTIAL DIFFERENTIAL EQUATIONS. Parabolic Problems. Hyperbolic Problems. Elliptic Problems. 16. MINIMIZATION OF FUNCTIONS. One-Variable Case. Multivariate Case. 17. LINEAR PROGRAMMING. Standard Forms and Duality. Simplex Method. Approximate Solution of Inconsistent Linear Systems. APPENDIX A. ADVICE ON GOOD PROGRAMMING PRACTICES. Programming Suggestions. APPENDIX B. REPRESENTATION OF NUMBERS IN DIFFERENT BASES. Representation of Numbers in Different Bases. APPENDIX C. ADDITIONAL DETAILS ON IEEE FLOATING-POINT ARITHMETIC. More on IEEE Standard Floating-Point Arithmetic. APPENDIX D. LINEAR ALGEBRA CONCEPTS AND NOTATION. Elementary Concepts. Abstract Vector Spaces. ANSWERS FOR SELECTED PROBLEMS. BIBLIOGRAPHY. INDEX.

About the Author

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).


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Amazon.com: 3.1 out of 5 stars 14 reviews
2 of 2 people found the following review helpful
2.0 out of 5 stars Very weak Numerical Methods Textbook 12 May 2015
By Jake - Published on Amazon.com
Format: Hardcover Verified Purchase
This book is mysteriously organized and lacking in key areas, notably in the polynomial regression chapters. There are numerous errors; the errata must be consulted frequently. The pseudocode is quite bizarre and not well explained in the accompanying text. Would not recommend.
3 of 4 people found the following review helpful
4.0 out of 5 stars This book is... pretty good 28 Feb. 2013
By adrukker - Published on Amazon.com
Format: Hardcover Verified Purchase
This book is pretty good. It is a lot nicer looking than the previous edition, but almost nothing was changed. The examples can be confusing at times. It is a difficult book for undergraduates, but for those with experience computing and writing code, it is not bad.
3 of 4 people found the following review helpful
2.0 out of 5 stars Very Difficult to Use 24 Nov. 2013
By Phillip D'Amore - Published on Amazon.com
Format: Hardcover Verified Purchase
This textbook is very vague in several of its descriptions and does not give enough clear examples. Would not recommend.
1.0 out of 5 stars This book is the worst of the worst 10 Dec. 2015
By Aron Vischjager - Published on Amazon.com
Format: Hardcover
This book is the worst of the worst. Most concepts are poorly explained and the examples in the book are never finished. In every section they present different examples but all the hard parts of every example are left for the reader as an exercise. So, they essentially don't give the reader any fully finished examples. I am currently taking a numerical analysis course and I am doing very well but this book is bad that I have learned more from watching Youtube videos than from reading this book!
1 of 2 people found the following review helpful
2.0 out of 5 stars Not Worth It 2 Oct. 2014
By Nyck - Published on Amazon.com
Format: Hardcover
Used this as a textbook for my senior-in-college-level numerical methods course. My first complaint is, of course, the cost. For ~$250, you'd expect to be getting something that not only took a lot of work to write, but also contained a wealth of useful information. Unfortunately, there were still numerical errors (STILL! AFTER 7 EDITIONS!) and confusing examples that aren't adequately explained. I tried to read and learn from this book- I really did. But in the end decided that the struggle was in vain. You can learn this material easier (and for free!) using one or more of the many many options online. MIT's OpenCourseWare has a wonderful series of lectures that you can watch.

I highly suggest avoiding this book because it's just not worth it. You'd be spending too much money for the ability to waste too much time on a subject that can be learned quicker and easier from freer sources
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