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by E. Ward Cheney and David R. Kincaid

ISBN13: 978-0534389932

ISBN10: 0534389937

Edition: 5TH 04

Copyright: 2004

Publisher: Brooks/Cole Publishing Co.

Published: 2004

International: No

ISBN10: 0534389937

Edition: 5TH 04

Copyright: 2004

Publisher: Brooks/Cole Publishing Co.

Published: 2004

International: No

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. The text also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors. A more theoretical text with a different menu of topics is the authors' highly regarded NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING, THIRD EDITION.

**Benefits: **

- NEW! New coverage of eigenvalues and eigenvectors, Newton-Cotes integration rules, Cholesky factorization, power methods, and the finite element method.
- NEW! More examples throughout, many involving the use of Matlab, Maple, or Mathematica. These systems illustrate some of the powerful software tools available for numerical, symbolic, and graphical computations.
- NEW! Additional exercises are included. Many more problems now have answers in the back of the book.
- NEW! Summaries appear at the end of each section.
- NEW! The appendices have been reorganized and new ones added. The appendix on an Overview of Mathematical Software Available on the World Wide Web has been brought up to date. Some material has been moved to the appendices such as programming suggestions and additional details on the IEEE floating-point standard.
- Numerous examples and problems are solved using either computations by hand, by using a calculator, or utilizing mathematical packages such as Matlab, Maple, and Mathematica.
- Problems are supplied in abundance to enhance the books versatility. They are divided into two categories: PROBLEMS and COMPUTER PROBLEMS. In the first category, more than 800 analysis exercises require pencil, paper, and possibly a calculator. In the second category, approximately 500 problems involve writing a program and testing it on a computer.
- Sample programs and other material supporting the text is available at: www.ma.utexas.edu/CNA/NMC5/
- Throughout the book, computer problems designated as STUDENT RESEARCH PROJECTS suggest opportunities for students to explore topics beyond the scope of the book.

Author Bio

**Cheney, E. Ward : University of Texas at Austin **

**Kincaid, David R. : University of Texas at Austin**

**1. INTRODUCTION. **

Preliminary Remarks.

Review of Taylor Series.

**2. NUMBER REPRESENTATION AND ERRORS. **

Representation of Numbers in Different Bases.

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. **

Definite Integral.

Trapezoid Rule.

Romberg Algorithm.

**6. MORE ON NUMERICAL INTEGRATION. **

An Adaptive Simpson's Scheme.

Gaussian Quadrature Formulas.

**7. SYSTEMS OF LINEAR EQUATIONS. **

Naive Gaussian Elimination.

Gaussian Elimination with Scaled Partial Pivoting.

Tridiagonal and Banded Systems.

**8. MORE ON SYSTEMS OF LINEAR EQUATIONS. **

Factorizations.

Iterative Solution of Linear Systems.

Eigenvalues and Eigenvectors.

Power Methods.

**9. APPROXIMATION BY SPLINE FUNCTIONS. **

First-Degree and Second-Degree Splines.

Natural Cubic Splines.

B splines: Interpolation and Approximation by B Splines.

**10. ORDINARY DIFFERENTIAL EQUATIONS. **

Initial-Value Problem: Analytical vs. Numerical Solution.

Taylor Series Methods.

Runge-Kutta Methods.

Stability and Adaptive Runge-Kutta and Multi-Step Methods.

**11. SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. **

Methods for First-Order Systems.

Higher-Order Equations and Systems.

Adams-Moulton Methods.

**12. SMOOTHING OF DATA AND THE METHOD OF LEAST SQUARES. **

The 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\hfill\break Monte Carlo Techniques.

Simulation.

**14. BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. **

Shooting Method.

A Discretization Method.

**15. PARTIAL DIFFERENTIAL EQUATIONS. **

Some Partial Differential Equations from Applied Problems.

Parabolic Problems.

Hyperbolic Problems.

Elliptic Problems.

**16. MINIMIZATION OF MULTIVARIATE FUNCTIONS. **

One-Variable Case.

Multivariate Case.

**17. LINEAR PROGRAMMING. **

Standard Forms and Duality.

Simplex Method.

Approximate Solution of Inconsistent Linear Systems.

**Appendices. **

Advice on Good Programming Practices.

An Overview of Mathematical Software on the Web.

Additional Details on IEEE Floating-Point Arithmetic.

Linear Algebra Concepts and Notation.

Sir Isaac Newton: Never at Rest.

Answers for Selected Problems.

Bibliography.

E. Ward Cheney and David R. Kincaid

ISBN13: 978-0534389932ISBN10: 0534389937

Edition: 5TH 04

Copyright: 2004

Publisher: Brooks/Cole Publishing Co.

Published: 2004

International: No

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. The text also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors. A more theoretical text with a different menu of topics is the authors' highly regarded NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING, THIRD EDITION.

**Benefits: **

- NEW! New coverage of eigenvalues and eigenvectors, Newton-Cotes integration rules, Cholesky factorization, power methods, and the finite element method.
- NEW! More examples throughout, many involving the use of Matlab, Maple, or Mathematica. These systems illustrate some of the powerful software tools available for numerical, symbolic, and graphical computations.
- NEW! Additional exercises are included. Many more problems now have answers in the back of the book.
- NEW! Summaries appear at the end of each section.
- NEW! The appendices have been reorganized and new ones added. The appendix on an Overview of Mathematical Software Available on the World Wide Web has been brought up to date. Some material has been moved to the appendices such as programming suggestions and additional details on the IEEE floating-point standard.
- Numerous examples and problems are solved using either computations by hand, by using a calculator, or utilizing mathematical packages such as Matlab, Maple, and Mathematica.
- Problems are supplied in abundance to enhance the books versatility. They are divided into two categories: PROBLEMS and COMPUTER PROBLEMS. In the first category, more than 800 analysis exercises require pencil, paper, and possibly a calculator. In the second category, approximately 500 problems involve writing a program and testing it on a computer.
- Sample programs and other material supporting the text is available at: www.ma.utexas.edu/CNA/NMC5/
- Throughout the book, computer problems designated as STUDENT RESEARCH PROJECTS suggest opportunities for students to explore topics beyond the scope of the book.

Author Bio

**Cheney, E. Ward : University of Texas at Austin **

**Kincaid, David R. : University of Texas at Austin**

Table of Contents

**1. INTRODUCTION. **

Preliminary Remarks.

Review of Taylor Series.

**2. NUMBER REPRESENTATION AND ERRORS. **

Representation of Numbers in Different Bases.

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. **

Definite Integral.

Trapezoid Rule.

Romberg Algorithm.

**6. MORE ON NUMERICAL INTEGRATION. **

An Adaptive Simpson's Scheme.

Gaussian Quadrature Formulas.

**7. SYSTEMS OF LINEAR EQUATIONS. **

Naive Gaussian Elimination.

Gaussian Elimination with Scaled Partial Pivoting.

Tridiagonal and Banded Systems.

**8. MORE ON SYSTEMS OF LINEAR EQUATIONS. **

Factorizations.

Iterative Solution of Linear Systems.

Eigenvalues and Eigenvectors.

Power Methods.

**9. APPROXIMATION BY SPLINE FUNCTIONS. **

First-Degree and Second-Degree Splines.

Natural Cubic Splines.

B splines: Interpolation and Approximation by B Splines.

**10. ORDINARY DIFFERENTIAL EQUATIONS. **

Initial-Value Problem: Analytical vs. Numerical Solution.

Taylor Series Methods.

Runge-Kutta Methods.

Stability and Adaptive Runge-Kutta and Multi-Step Methods.

**11. SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. **

Methods for First-Order Systems.

Higher-Order Equations and Systems.

Adams-Moulton Methods.

**12. SMOOTHING OF DATA AND THE METHOD OF LEAST SQUARES. **

The 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\hfill\break Monte Carlo Techniques.

Simulation.

**14. BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. **

Shooting Method.

A Discretization Method.

**15. PARTIAL DIFFERENTIAL EQUATIONS. **

Some Partial Differential Equations from Applied Problems.

Parabolic Problems.

Hyperbolic Problems.

Elliptic Problems.

**16. MINIMIZATION OF MULTIVARIATE FUNCTIONS. **

One-Variable Case.

Multivariate Case.

**17. LINEAR PROGRAMMING. **

Standard Forms and Duality.

Simplex Method.

Approximate Solution of Inconsistent Linear Systems.

**Appendices. **

Advice on Good Programming Practices.

An Overview of Mathematical Software on the Web.

Additional Details on IEEE Floating-Point Arithmetic.

Linear Algebra Concepts and Notation.

Sir Isaac Newton: Never at Rest.

Answers for Selected Problems.

Bibliography.

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