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Table of Contents
1 Cover
4 Preface to the Solutions Manual for the Third Edition
5 CHAPTER 1: INTRODUCTORY CONCEPTS AND CALCULUS REVIEW 1.1 BASIC TOOLS OF CALCULUS 1.2 ERROR, APPROXIMATE EQUALITY, AND ASYMPTOTIC ORDER NOTATION 1.3 A PRIMER ON COMPUTER ARITHMETIC 1.4 A WORD ON COMPUTER LANGUAGES AND SOFTWARE 1.5 A BRIEF HISTORY OF SCIENTIFIC COMPUTING
6 Chapter 2: A SURVEY OF SIMPLE METHODS AND TOOLS 2.1 HORNER'S RULE AND NESTED MULTIPLICATION 2.2 DIFFERENCE APPROXIMATIONS TO THE DERIVATIVE 2.3 APPLICATION: EULER'S METHOD FOR INITIAL VALUE PROBLEMS 2.4 LINEAR INTERPOLATION 2.5 APPLICATION — THE TRAPEZOID RULE 2.6 SOLUTION OF TRIDIAGONAL LINEAR SYSTEMS 2.7 APPLICATION: SIMPLE TWO‐POINT BOUNDARY VALUE PROBLEMS
7 CHAPTER 3: ROOT‐FINDING 3.1 THE BISECTION METHOD 3.2 NEWTON'S METHOD: DERIVATION AND EXAMPLES 3.3 HOW TO STOP NEWTON'S METHOD 3.4 APPLICATION: DIVISION USING NEWTON'S METHOD 3.5 THE NEWTON ERROR FORMULA 3.6 NEWTON'S METHOD: THEORY AND CONVERGENCE 3.7 APPLICATION: COMPUTATION OF THE SQUARE ROOT 3.8 THE SECANT METHOD: DERIVATION AND EXAMPLES 3.9 FIXED POINT ITERATION 3.10 ROOTS OF POLYNOMIALS (PART 1) 3.11 SPECIAL TOPICS IN ROOT‐FINDING METHODS 3.12 VERY HIGH‐ORDER METHODS AND THE EFFICIENCY INDEX NOTES
8 CHAPTER 4: INTERPOLATION AND APPROXIMATION 4.1 LAGRANGE INTERPOLATION 4.2 NEWTON INTERPOLATION AND DIVIDED DIFFERENCES 4.3 INTERPOLATION ERROR 4.4 APPLICATION: MULLER'S METHOD AND INVERSE QUADRATIC INTERPOLATION 4.5 APPLICATION: MORE APPROXIMATIONS TO THE DERIVATIVE 4.6 HERMITE INTERPOLATION 4.7 PIECEWISE POLYNOMIAL INTERPOLATION 4.8 AN INTRODUCTION TO SPLINES 4.9 TENSION SPLINES 4.10 LEAST SQUARES CONCEPTS IN APPROXIMATION 4.11 ADVANCED TOPICS IN INTERPOLATION ERROR NOTES
9 CHAPTER 5: NUMERICAL INTEGRATION 5.1 A REVIEW OF THE DEFINITE INTEGRAL 5.2 IMPROVING THE TRAPEZOID RULE 5.3 SIMPSON'S RULE AND DEGREE OF PRECISION 5.4 THE MIDPOINT RULE 5.5 APPLICATION: STIRLING'S FORMULA 5.6 GAUSSIAN QUADRATURE 5.7 EXTRAPOLATION METHODS 5.8 SPECIAL TOPICS IN NUMERICAL INTEGRATION
10 CHAPTER 6: NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 6.1 The Initial Value Problem—Background 6.2 Euler's Method 6.3 Analysis of Euler's Method 6.4 Variants of Euler's Method 6.5 Single Step Methods—Runge‐Kutta 6.6 Multistep Methods 6.7 Stability Issues 6.8 Application to Systems of Equations 6.9 Adaptive Solvers 6.10 Boundary Value Problems NOTE
11 CHAPTER 7: NUMERICAL METHODS FOR THE SOLUTION OF SYSTEMS OF EQUATIONS 7.1 LINEAR ALGEBRA REVIEW 7.2 LINEAR SYSTEMS AND GAUSSIAN ELIMINATION 7.3 OPERATION COUNTS 7.4 THE FACTORIZATION 7.5 PERTURBATION, CONDITIONING