by Ward Cheney and David Kincaid

ISBN13: 978-0534351847

ISBN10: 0534351840

Cover type:

Edition/Copyright: 4TH 99

Publisher: Brooks/Cole Publishing Co.

Published: 1999

International: No

ISBN10: 0534351840

Cover type:

Edition/Copyright: 4TH 99

Publisher: Brooks/Cole Publishing Co.

Published: 1999

International: No

This book acquaints students of science and engineering with the modern computer's potential for solving the numerical problems that will arise in their careers. It also gives students an opportunity to hone their skills in programming and problem solving. It helps them arrive at an understanding of the important subject of errors that inevitably accompany scientific computing and arms them with methods for detecting, predicting, and controlling these errors.

Language-independent computer algorithms provide an emphasis on mathematical algorithms rather than on the computer language used to implement them.

Numerous solved examples, using either Maple V or MATLAB, illustrate just two of the powerful software tools available for symbolic, numeric, and graphical results.

Displayed pseudocode, coded in several programming languages, is available by anonymous ftp from ftp.brookscole.com.

Computer-code fragments and numerous examples make the material accessible to students.

A wide diversity of topics, including some advanced ones that play an important role in current scientific computing, give students a survey of numerical mathematics.

Two categories of problems enhance the text's versatility: "Problems" and "Computer Problems." The first category contains more than 800 exercises in analysis that require pencil, paper, and possibly a calculator. The second category includes about 450 problems that involve writing a program and testing it on the computer.

Suggested student projects stimulate students to go outside the text for additional information. Such projects provide experience in discovering recent research in the subject of numerical computation.

A long and detailed discussion of how to locate codes on the World Wide Web. This section gives pointers to the principal archives of software, especially software that is available without payment of fees.

Additional discussion of search methods for optimization problems are included. The Nelder-Meade Algorithm and the method of Simulated Annealing have been added.

Improved examples illustrate realistic problems in computing.

Many new problems of an analytic or computational nature give students practice.

A new section on iterative methods for solving large systems of linear equations has been added.

Additional explanatory material for difficult concepts appears throughout. This should be especially helpful for students engaged in solo study.

The authors have made many improvements to the pseudocode for all algorithms. The pseudocode can be readily turned into codes in C, C++, Fortran, Pascal, or other programming languages.

The authors have improved the arrangement of problems to put similar ones together.

The authors now cover additional material on classical polynomial interpolation, including the Neville algorithm.

Additional discussion of the current IEEE standards for floating-point operations in 32-bit machines has been added.

"I have to say that I have looked at a dozen or so books and [this] seems to be the best. Some of the best features: good choice of subjects, well written, virtually no misprints, easy to understand, many good examples . . . extensive and good choices of exercises and good answer book. [It] makes a good reference."

Robert E. Funderlic, North Carolina State University

"My overall impression is that [the text] presents the material more clearly, usually without unnecessary generality and without burying the ideas in too much notation. Students at this level can be 'blown away' just by notational matters. This book avoids this most of the time, especially when presenting the basic mathematical discussions of the numerical methods considered. I have also found the material devoted to the derivations of the methods very well written."

Marcus Wright, Rowan College of New Jersey

Author Bio

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

**1. INTRODUCTION. **

Preliminary Remarks.

Programming Suggestions.

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.

An Adaptive Simpson's Sceme.

Gaussian Quadrature Formulas.

**6. SYSTEMS OF LINEAR EQUATIONS. **

Naive Gaussian Elimination.

Gaussian Elimination with Scaled Partial Pivoting.

Tridiagonal and Banded Systems.

LU Factorization.

**7. APPROXIMATION BY SPLINE FUNCTIONS. **

First-Degree and Second-Degree Splines.

Natural Cubic Splines.

B Splines.

Interpolation and Approximation by B Splines.

**8. ORDINARY DIFFERENTIAL EQUATIONS. **

Initial-Value Problem: Analytical vs. Numerical Solution.

Taylor Series Methods.

Runge-Kutta Methods.

Stability and Adaptive Runge-Kutta Methods.

**9. SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. **

Methods for First-Order Systems.

Higher-Order Equations and Systems.

Adams-Moulton Methods.

**10. 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 Priciple.

**11. MONTE CARLO METHODS AND SIMULATION. **

Random Numbers.

Estimation of Areas and Volumes by Monte Carlo Techniques.

Simulation.

**12. BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATION. **

Shooting Method.

A Discretization Method.

**13. PARTIAL DIFFERENTIAL EQUATIONS. **

Some Partial Differential Equations from Applied Problems.

Parabolic Problems.

Hyperbolic Problems.

Elliptic Problems.

**14. MINIMIZATION OF MULTIVARIATE FUNCTIONS. **

Unconstrained and Constrained Minimization Problems.

One-Variable Case.

Multivariate Case.

**15. LINEAR PROGRAMMING. **

Standard Forms and Duality.

Simplex Method.

Approximate Solution of Inconsistent Linear Systems.

Appendix A: Linear Algebra Concepts and Notation.

Answers for Selected Problems.

Bibliography.

Index

ISBN10: 0534351840

Cover type:

Edition/Copyright: 4TH 99

Publisher: Brooks/Cole Publishing Co.

Published: 1999

International: No

This book acquaints students of science and engineering with the modern computer's potential for solving the numerical problems that will arise in their careers. It also gives students an opportunity to hone their skills in programming and problem solving. It helps them arrive at an understanding of the important subject of errors that inevitably accompany scientific computing and arms them with methods for detecting, predicting, and controlling these errors.

Language-independent computer algorithms provide an emphasis on mathematical algorithms rather than on the computer language used to implement them.

Numerous solved examples, using either Maple V or MATLAB, illustrate just two of the powerful software tools available for symbolic, numeric, and graphical results.

Displayed pseudocode, coded in several programming languages, is available by anonymous ftp from ftp.brookscole.com.

Computer-code fragments and numerous examples make the material accessible to students.

A wide diversity of topics, including some advanced ones that play an important role in current scientific computing, give students a survey of numerical mathematics.

Two categories of problems enhance the text's versatility: "Problems" and "Computer Problems." The first category contains more than 800 exercises in analysis that require pencil, paper, and possibly a calculator. The second category includes about 450 problems that involve writing a program and testing it on the computer.

Suggested student projects stimulate students to go outside the text for additional information. Such projects provide experience in discovering recent research in the subject of numerical computation.

A long and detailed discussion of how to locate codes on the World Wide Web. This section gives pointers to the principal archives of software, especially software that is available without payment of fees.

Additional discussion of search methods for optimization problems are included. The Nelder-Meade Algorithm and the method of Simulated Annealing have been added.

Improved examples illustrate realistic problems in computing.

Many new problems of an analytic or computational nature give students practice.

A new section on iterative methods for solving large systems of linear equations has been added.

Additional explanatory material for difficult concepts appears throughout. This should be especially helpful for students engaged in solo study.

The authors have made many improvements to the pseudocode for all algorithms. The pseudocode can be readily turned into codes in C, C++, Fortran, Pascal, or other programming languages.

The authors have improved the arrangement of problems to put similar ones together.

The authors now cover additional material on classical polynomial interpolation, including the Neville algorithm.

Additional discussion of the current IEEE standards for floating-point operations in 32-bit machines has been added.

"I have to say that I have looked at a dozen or so books and [this] seems to be the best. Some of the best features: good choice of subjects, well written, virtually no misprints, easy to understand, many good examples . . . extensive and good choices of exercises and good answer book. [It] makes a good reference."

Robert E. Funderlic, North Carolina State University

"My overall impression is that [the text] presents the material more clearly, usually without unnecessary generality and without burying the ideas in too much notation. Students at this level can be 'blown away' just by notational matters. This book avoids this most of the time, especially when presenting the basic mathematical discussions of the numerical methods considered. I have also found the material devoted to the derivations of the methods very well written."

Marcus Wright, Rowan College of New Jersey

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.

Programming Suggestions.

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.

An Adaptive Simpson's Sceme.

Gaussian Quadrature Formulas.

**6. SYSTEMS OF LINEAR EQUATIONS. **

Naive Gaussian Elimination.

Gaussian Elimination with Scaled Partial Pivoting.

Tridiagonal and Banded Systems.

LU Factorization.

**7. APPROXIMATION BY SPLINE FUNCTIONS. **

First-Degree and Second-Degree Splines.

Natural Cubic Splines.

B Splines.

Interpolation and Approximation by B Splines.

**8. ORDINARY DIFFERENTIAL EQUATIONS. **

Initial-Value Problem: Analytical vs. Numerical Solution.

Taylor Series Methods.

Runge-Kutta Methods.

Stability and Adaptive Runge-Kutta Methods.

**9. SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. **

Methods for First-Order Systems.

Higher-Order Equations and Systems.

Adams-Moulton Methods.

**10. 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 Priciple.

**11. MONTE CARLO METHODS AND SIMULATION. **

Random Numbers.

Estimation of Areas and Volumes by Monte Carlo Techniques.

Simulation.

**12. BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATION. **

Shooting Method.

A Discretization Method.

**13. PARTIAL DIFFERENTIAL EQUATIONS. **

Some Partial Differential Equations from Applied Problems.

Parabolic Problems.

Hyperbolic Problems.

Elliptic Problems.

**14. MINIMIZATION OF MULTIVARIATE FUNCTIONS. **

Unconstrained and Constrained Minimization Problems.

One-Variable Case.

Multivariate Case.

**15. LINEAR PROGRAMMING. **

Standard Forms and Duality.

Simplex Method.

Approximate Solution of Inconsistent Linear Systems.

Appendix A: Linear Algebra Concepts and Notation.

Answers for Selected Problems.

Bibliography.

Index

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