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Numerical Mathematics and Computing, International Edition

저자 : Cheney/Kincaid | 출간 연도 : 2013

ISBN 9781133491811 (1133491812)
저자 Cheney/Kincaid
출간 연도 2013
7E
페이지 704쪽
크기 8 X 10
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원서 ISBN 9781133491811
책소개 목차 원서정보 오탈자 강의자료
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, 7E, International Edition also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors.
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.
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 Ser
Solution Builder for Cheney/Kincaid's Numerical Mathematics and Computing, 7th, 007e, 9781133491798 Student Solutions Manual for Cheney/Kincaid's Numerical Mathematics and Computing, 7th, 007e, 9781133491804 Web Site for Cheney/Kincaid's Numerical Mathema