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Record Nr. |
UNINA9910795812903321 |
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Autore |
Epperson James F |
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Titolo |
Solutions Manual to Accompany an Introduction to Numerical Methods and Analysis |
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Pubbl/distr/stampa |
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Somerset : , : John Wiley & Sons, Incorporated, , 2013 |
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©2014 |
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ISBN |
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9781118552131 |
9781118789377 |
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Edizione |
[2nd ed.] |
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Descrizione fisica |
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1 online resource (319 pages) |
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Disciplina |
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Soggetti |
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Numerical analysis -- Handbooks, manuals, etc |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Cover page -- Half-Title page -- Title page -- Copyright page -- CONTENTS -- Preface to the Solutions Manual -- 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 SIMPLE APPROXIMATIONS -- 1.6 APPLICATION: APPROXIMATING THE NATURAL LOGARITHM -- 1.7 A BRIEF HISTORY OF COMPUTING -- 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 -- 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 |
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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 -- 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 APPLICATION: SOLUTION OF BOUNDARY VALUE PROBLEMS -- 4.10 TENSION SPLINES. |
4.11 LEAST SQUARES CONCEPTS IN APPROXIMATION -- 4.12 ADVANCED TOPICS IN INTERPOLATION ERROR -- 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 -- 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 MULTI-STEP METHODS -- 6.7 STABILITY ISSUES -- 6.8 APPLICATION TO SYSTEMS OF EQUATIONS -- 6.9 ADAPTIVE SOLVERS -- 6.10 BOUNDARY VALUE PROBLEMS -- CHAPTER 7: NUMERICAL METHODS FOR THE SOLUTION OF SYSTEMS OF EQUATIONS -- 7.1 LINEAR ALGEBRA REVIEW -- 7.2 LINEAR SYSTEMS AND GAUSSIAN ELIMINATION Exercises: -- 7.3 OPERATION COUNTS -- 7.4 THE LU FACTORIZATION -- 7.5 PERTURBATION, CONDITIONING AND STABILITY -- 7.6 S P D MATRICES AND THE CHOLESKY DECOMPOSITION -- 7.7 ITERATIVE METHODS FOR LINEAR SYSTEMS - A BRIEF SURVEY -- 7.8 NONLINEAR SYSTEMS: NEWTON'S METHOD AND RELATED IDEAS -- 7.9 APPLICATION: NUMERICAL SOLUTION OF NONLINEAR BVP'S -- CHAPTER 8: APPROXIMATE SOLUTION OF THE ALGEBRAIC EIGENVALUE PROBLEM -- 8.1 EIGENVALUE REVIEW -- 8.2 REDUCTION TO HESSENBERG FORM -- 8.3 POWER METHODS -- 8.4 AN OVERVIEW OF THE Q R ITERATION -- 8.5 APPLICATION: ROOTS OF POLYNOMIALS, II -- CHAPTER 9: A SURVEY OF NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS -- 9.1 DIFFERENCE METHODS FOR THE DIFFUSION EQUATION -- 9.2 FINITE ELEMENT METHODS FOR THE DIFFUSION EQUATION -- 9.3 DIFFERENCE METHODS FOR POISSON EQUATIONS -- CHAPTER 10: AN INTRODUCTION TO SPECTRAL METHODS. |
10.1 SPECTRAL METHODS FOR TWO-POINT BOUNDARY VALUE PROBLEMS -- 10.2 SPECTRAL METHODS FOR TIME-DEPENDENT PROBLEMS -- 10.3 CLENSHAW-CURTIS QUADRATURE. |
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Sommario/riassunto |
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A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and theSecond Edition also features: Chapters and sections that begin with |
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basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB® An appendix that contains proofs of various theorems and other material. |
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