Solutions Manual to accompany An Introduction to Numerical Methods and Analysis /

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Detalles Bibliográficos
Autor principal: Epperson, James F.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: [Place of publication not identified] John Wiley & Sons, Incorporated, 2013.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Contents
  • Title Page
  • Copyright
  • 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 Exercises:
  • 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 Exercises:
  • 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
  • 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
  • 7.3 OPERATION COUNTS
  • 7.4 THE LU FACTORIZATION
  • 7.5 PERTURBATION, CONDITIONING AND STABILITY

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