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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.
- UPDATED! The Solving Systems of Linear Equations chapter has been moved earlier in the text to provide more clarity throughout the text.
- 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.
- 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.
- 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 two chapters, in the previous edition, on Ordinary Differential Equations have been combined into one chapter.
- Many of the pseudocodes from the text have been programmed in MATLAB, Mathematica, and Maple and appear in the website so that they are easily accessible.
- More figures and numerical examples have been added.
- 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.
- 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.
- 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.
- 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.
Introduction, Mathematical Preliminaries. Floating-Point Representation. Loss of Significance.
2. LINEAR SYSTEMS.
Naive Gaussian Elimination. Gaussian Elimination with Scaled Partial Pivoting. Tridiagonal and Banded Systems.
3. NONLINEAR EQUATIONS.
Bisection Method. Newton’s Method, Secant Method.
4. INTERPOLATION AND NUMBERICAL DIFFERENTIATION.
Polynomial Interpolation. Errors in Polynomial Interpolation. Estimating Derivatives and Richardson Extrapolation.
5. NUMERICAL INTEGRATION.
Trapezoid Method. Romberg Algorithm. Simpson’s Rules and Newton-Cotes Rules. Gaussian Quadrature Formulas.
6. SPLINE FUNCTIONS.
First-Degree and Second-Degree Splines. Natural Cubic Splines. B Splines: Interpolation and Approximation.
7. INITIAL VALUES PROBLEMS.
Taylor Series Methods. Runge-Kutta Methods. Adaptive Runge-Kutta and Multistep Methods. Methods for First and Higher-Order Systems. Adams-Bashforth-Moulton Methods.
8. MORE ON LINEAR SYSTEMS.
Matrix Factorizations. Eigenvalues and Eigenvectors. Power Method. Iterative Solutions of Linear Systems.
9. LEAST SQUARES METHODS AND FOURIER SERIES.
Method of Least Squares. Orthogonal Systems and Chebyshev Polynomials. Examples of the Least-Squares Principle. Fourier Series.
10. MONTE CARLO METHODS AND SIMULATION.
Random Numbers. Estimation of Areas and Volumes by Monte Carlo Techniques. Simulation.
11. BOUNDARY-VALUE PROBLEMS.
Shooting Method. A Discretization Method.
12. PARTIAL DIFFERENTIAL EQUATIONS.
Parabolic Problems. Hyperbolic Problems. Elliptic Problems.
13. MINIMIZATION OF FUNTIONS.
One-Variable Case. Multivariable Case.
14. LINEAR PROGRAMMING PROBLEMS.
Standard Forms and Duality. Simplex Method, Inconsistent Linear Systems.
APPENDIX A. ADVICE ON GOOD PROGRAMMING PRACTICES.
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.
ANSWERS FOR SELECTED EXERCISES.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
This online instructor database offers complete worked solutions to all exercises in the text, allowing you to create customized, secure solutions printouts (in PDF format) matched exactly to the problems you assign in class. Visit Cengage.com/solutionbuilder for more information.
Instructors Solutions Manual
Student Solutions Manual
Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
Student Solutions Manual
Go beyond the answers—see what it takes to get there and improve your grade! This manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. This gives you the information you need to truly understand how these problems are solved.