Numerical Mathematics and Computing
7th Edition
Published on 24. November 2020
Book
Paperback/Softback
704 pages
978-0-357-67084-2 (ISBN)
Description
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.
More details
Edition
7th edition
Language
English
Place of publication
CA
United States
Publishing group
Cengage Learning, Inc
Target group
College/higher education
Dimensions
Height: 27 mm
Width: 203 mm
Thickness: 254 mm
Weight
1293 gr
ISBN-13
978-0-357-67084-2 (9780357670842)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
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).
Content
1. MATHEMATICAL PRELIMINARIES AND FLOATING-POINT REPRESENTATION.
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.
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.
ANSWERS FOR SELECTED EXERCISES.
BIBLIOGRAPHY.
INDEX.
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.
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.
ANSWERS FOR SELECTED EXERCISES.
BIBLIOGRAPHY.
INDEX.