Solutions Manual to Accompany An Introduction to Numerical Methods and Analysis

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James F. Epperson. Solutions Manual to Accompany An Introduction to Numerical Methods and Analysis

Table of Contents

List of Tables

List of Illustrations

Guide

Pages

Solutions Manual to Accompany. An Introduction to Numerical Methods and Analysis

Preface to the Solutions Manual for the Third Edition

CHAPTER 1 INTRODUCTORY CONCEPTS AND CALCULUS REVIEW. 1.1 BASIC TOOLS OF CALCULUS. Exercises:

1.2 ERROR, APPROXIMATE EQUALITY, AND ASYMPTOTIC ORDER NOTATION. Exercises:

1.3 A PRIMER ON COMPUTER ARITHMETIC. Exercises:

1.4 A WORD ON COMPUTER LANGUAGES AND SOFTWARE

1.5 A BRIEF HISTORY OF SCIENTIFIC COMPUTING

Chapter 2 A SURVEY OF SIMPLE METHODS AND TOOLS. 2.1 HORNER'S RULE AND NESTED MULTIPLICATION. Exercises:

2.2 DIFFERENCE APPROXIMATIONS TO THE DERIVATIVE. Exercises:

2.3 APPLICATION: EULER'S METHOD FOR INITIAL VALUE PROBLEMS. Exercises:

2.4 LINEAR INTERPOLATION. Exercises:

2.5 APPLICATION — THE TRAPEZOID RULE. Exercises:

2.6 SOLUTION OF TRIDIAGONAL LINEAR SYSTEMS. Exercises:

2.7 APPLICATION: SIMPLE TWO‐POINT BOUNDARY VALUE PROBLEMS. Exercises:

CHAPTER 3 ROOT‐FINDING

3.1 THE BISECTION METHOD. Exercises:

3.2 NEWTON'S METHOD: DERIVATION AND EXAMPLES. Exercises:

3.3 HOW TO STOP NEWTON'S METHOD. Exercises:

3.4 APPLICATION: DIVISION USING NEWTON'S METHOD. Exercises:

3.5 THE NEWTON ERROR FORMULA. Exercises:

3.6 NEWTON'S METHOD: THEORY AND CONVERGENCE. Exercises:

3.7 APPLICATION: COMPUTATION OF THE SQUARE ROOT. Exercises:

3.8 THE SECANT METHOD: DERIVATION AND EXAMPLES. Exercises:

3.9 FIXED POINT ITERATION. Exercises:

3.10 ROOTS OF POLYNOMIALS (PART 1) Exercises:

3.11 SPECIAL TOPICS IN ROOT‐FINDING METHODS. Exercises:

3.12 VERY HIGH‐ORDER METHODS AND THE EFFICIENCY INDEX. Exercises:

NOTES

CHAPTER 4. INTERPOLATION AND APPROXIMATION. 4.1 LAGRANGE INTERPOLATION. Exercises:

4.2 NEWTON INTERPOLATION AND DIVIDED DIFFERENCES. Exercises:

4.3 INTERPOLATION ERROR. Exercises:

4.4 APPLICATION: MULLER'S METHOD AND INVERSE QUADRATIC INTERPOLATION. Exercises

4.5 APPLICATION: MORE APPROXIMATIONS TO THE DERIVATIVE. Exercises:

4.6 HERMITE INTERPOLATION. Exercises:

4.7 PIECEWISE POLYNOMIAL INTERPOLATION. Exercises:

4.8 AN INTRODUCTION TO SPLINES. Exercises:

4.9 TENSION SPLINES. Exercises:

4.10 LEAST SQUARES CONCEPTS IN APPROXIMATION. Exercises:

4.11 ADVANCED TOPICS IN INTERPOLATION ERROR. Exercises:

NOTES

CHAPTER 5 NUMERICAL INTEGRATION. 5.1 A REVIEW OF THE DEFINITE INTEGRAL. Exercises:

5.2 IMPROVING THE TRAPEZOID RULE. Exercises:

5.3 SIMPSON'S RULE AND DEGREE OF PRECISION. Exercises:

5.4 THE MIDPOINT RULE. Exercises:

5.5 APPLICATION: STIRLING'S FORMULA. Exercises:

5.6 GAUSSIAN QUADRATURE. Exercises:

5.7 EXTRAPOLATION METHODS. Exercises:

5.8 SPECIAL TOPICS IN NUMERICAL INTEGRATION. Exercises:

CHAPTER 6. NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS. 6.1 The Initial Value Problem—Background. Exercises:

6.2 Euler's Method. Exercises:

6.3 Analysis of Euler's Method. Exercises:

6.4 Variants of Euler's Method. Exercises:

6.5 Single Step Methods—Runge‐Kutta. Exercises:

6.6 Multistep Methods. Exercises:

6.7 Stability Issues. Exercises:

6.8 Application to Systems of Equations. Exercises:

6.9 Adaptive Solvers. Exercises

6.10 Boundary Value Problems. Exercises:

NOTE

CHAPTER 7. NUMERICAL METHODS FOR THE SOLUTION OF SYSTEMS OF EQUATIONS. 7.1 LINEAR ALGEBRA REVIEW. Exercises:

7.2 LINEAR SYSTEMS AND GAUSSIAN ELIMINATION. Exercises:

7.3 OPERATION COUNTS. Exercises:

7.4 THE FACTORIZATION. Exercises:

7.5 PERTURBATION, CONDITIONING AND STABILITY. Exercises:

7.6 SPD MATRICES AND THE CHOLESKY DECOMPOSITION. Exercises:

7.7 APPLICATION: NUMERICAL SOLUTION OF LINEAR LEAST SQUARES PROBLEMS. Exercises:

7.8 SPARSE AND STRUCTURED MATRICES

7.9 ITERATIVE METHODS FOR LINEAR SYSTEMS – A BRIEF SURVEY. Exercises:

7.10 NONLINEAR SYSTEMS: NEWTON'S METHOD AND RELATED IDEAS. Exercises:

7.11 APPLICATION: NUMERICAL SOLUTION OF NONLINEAR BVP's. Exercises:

CHAPTER 8. APPROXIMATE SOLUTION OF THE ALGEBRAIC EIGENVALUE PROBLEM. 8.1 EIGENVALUE REVIEW. Exercises:

8.2 REDUCTION TO HESSENBERG FORM. Exercises:

8.3 POWER METHODS. Exercises:

8.4 BISECTION AND INERTIA TO COMPUTE EIGENVALUES OF SYMMETRIC MATRICES. Exercises:

8.5 AN OVERVIEW OF THE ITERATION. Exercises:

8.6 APPLICATION: ROOTS OF POLYNOMIALS, II. Exercises:

8.7 APPLICATION: COMPUTATION OF GAUSSIAN QUADRATURE RULES. Exercises:

NOTE

CHAPTER 9 A SURVEY OF NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS. 9.1 DIFFERENCE METHODS FOR THE DIFFUSION EQUATION. Exercises:

9.2 FINITE ELEMENT METHODS FOR THE DIFFUSION EQUATION. Exercises:

9.3 DIFFERENCE METHODS FOR POISSON EQUATIONS. Exercises:

NOTE

CHAPTER 10 AN INTRODUCTION TO SPECTRAL METHODS. 10.1 SPECTRAL METHODS FOR TWO‐POINT BOUNDARY VALUE PROBLEMS. Exercises:

10.2 SPECTRAL METHODS IN TWO DIMENSIONS. Exercises:

10.3 SPECTRAL METHODS FOR TIME‐DEPENDENT PROBLEMS. Exercises:

10.4 CLENSHAW‐CURTIS QUADRATURE. Exercises:

WILEY END USER LICENSE AGREEMENT

Отрывок из книги

THIRD EDITION

James F. Epperson

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The author freely admits the potential for error in any of these solutions, especially since many of the exercises were modified after the final version of the text was submitted to the publisher and because the ordering of the exercises was changed between editions. While we tried to make all the appropriate corrections, the possibility of error is still present, and undoubtedly the author's responsibility.

Because much of the manual was constructed by doing “copy‐and‐paste” from the files for the text, the enumeration of many tables and figures will be different. I have tried to note what the number is in the text, but certainly may have missed some instances.

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