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An Introduction to Numerical Methods and Analysis
| An Introduction to Numerical Methods and Analysis |
| Autore | Epperson James F |
| Pubbl/distr/stampa | John Wiley & Sons, Incorporated |
| ISBN |
1118730968
9781118730966 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910595344003321 |
Epperson James F
|
||
| John Wiley & Sons, Incorporated | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An Introduction to Numerical Methods and Analysis, Second Edition [[electronic resource]]
| An Introduction to Numerical Methods and Analysis, Second Edition [[electronic resource]] |
| Autore | Epperson James F |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, : Wiley, 2013 |
| Descrizione fisica | 1 online resource (1171 p.) |
| Disciplina | 535.278 |
| Soggetto topico |
Lagrange equations
Mathematics Numerical analysis |
| ISBN |
1-118-73097-6
1-118-40746-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Half Title page; Title page; Copyright page; Dedication; Preface; 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; 1.8 Literature Review; References; 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 Problems2.4 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 Examples; 3.9 Fixed-Point Iteration 3.10 Roots of Polynomials, Part 13.11 Special Topics in Root-Finding Methods; 3.12 Very High-Order Methods and the Efficiency Index; 3.13 Literature and Software Discussion; References; 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 Problems4.10 Tension Splines; 4.11 Least Squares Concepts in Approximation; 4.12 Advanced Topics in Interpolation Error; 4.13 Literature and Software Discussion; References; 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; 5.9 Literature and Software Discussion; References Chapter 6: Numerical Methods for Ordinary Differential Equations6.1 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; 6.11 Literature and Software Discussion; References; 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 |
| Record Nr. | UNINA-9910787627903321 |
|
Epperson James F
|
||
| Hoboken, : Wiley, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An Introduction to Numerical Methods and Analysis, Second Edition
| An Introduction to Numerical Methods and Analysis, Second Edition |
| Autore | Epperson James F |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, : Wiley, 2013 |
| Descrizione fisica | 1 online resource (1171 p.) |
| Disciplina | 535.278 |
| Soggetto topico |
Lagrange equations
Mathematics Numerical analysis |
| ISBN |
1-118-73097-6
1-118-40746-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Half Title page; Title page; Copyright page; Dedication; Preface; 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; 1.8 Literature Review; References; 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 Problems2.4 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 Examples; 3.9 Fixed-Point Iteration 3.10 Roots of Polynomials, Part 13.11 Special Topics in Root-Finding Methods; 3.12 Very High-Order Methods and the Efficiency Index; 3.13 Literature and Software Discussion; References; 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 Problems4.10 Tension Splines; 4.11 Least Squares Concepts in Approximation; 4.12 Advanced Topics in Interpolation Error; 4.13 Literature and Software Discussion; References; 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; 5.9 Literature and Software Discussion; References Chapter 6: Numerical Methods for Ordinary Differential Equations6.1 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; 6.11 Literature and Software Discussion; References; 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 |
| Record Nr. | UNINA-9910824482203321 |
|
Epperson James F
|
||
| Hoboken, : Wiley, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Solutions Manual to Accompany An Introduction to Numerical Methods and Analysis [[electronic resource]]
| Solutions Manual to Accompany An Introduction to Numerical Methods and Analysis [[electronic resource]] |
| Autore | Epperson James F |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, : Wiley, 2014 |
| Descrizione fisica | 1 online resource (319 p.) |
| Disciplina | 518 |
| Soggetto topico |
Mathematics
Numerical analysis -- Handbooks, manuals, etc Numerical analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-55213-X
1-118-78937-7 1-118-78938-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 PROBLEMS2.4 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 EXAMPLES 3.9 FIXED POINT ITERATION3.10 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 SPLINES4.11 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 METHOD6.5 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 |
| Record Nr. | UNINA-9910458435803321 |
|
Epperson James F
|
||
| Hoboken, : Wiley, 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Solutions Manual to Accompany an Introduction to Numerical Methods and Analysis
| Solutions Manual to Accompany an Introduction to Numerical Methods and Analysis |
| Autore | Epperson James F |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Somerset : , : John Wiley & Sons, Incorporated, , 2013 |
| Descrizione fisica | 1 online resource (319 pages) |
| Disciplina | 518 |
| Soggetto topico | Numerical analysis -- Handbooks, manuals, etc |
| Soggetto genere / forma | Electronic books. |
| ISBN |
9781118552131
9781118789377 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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. |
| Record Nr. | UNINA-9910795812903321 |
|
Epperson James F
|
||
| Somerset : , : John Wiley & Sons, Incorporated, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Solutions Manual to Accompany an Introduction to Numerical Methods and Analysis
| Solutions Manual to Accompany an Introduction to Numerical Methods and Analysis |
| Autore | Epperson James F |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Somerset : , : John Wiley & Sons, Incorporated, , 2013 |
| Descrizione fisica | 1 online resource (319 pages) |
| Disciplina | 518 |
| Soggetto topico | Numerical analysis -- Handbooks, manuals, etc |
| Soggetto genere / forma | Electronic books. |
| ISBN |
9781118552131
9781118789377 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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. |
| Record Nr. | UNINA-9910823161303321 |
|
Epperson James F
|
||
| Somerset : , : John Wiley & Sons, Incorporated, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Solutions Manual to Accompany An Introduction to Numerical Methods and Analysis, Second Edition [[electronic resource]]
| Solutions Manual to Accompany An Introduction to Numerical Methods and Analysis, Second Edition [[electronic resource]] |
| Autore | Epperson James F |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, : Wiley, 2013 |
| Descrizione fisica | 1 online resource (1171 p.) |
| Disciplina | 535.278 |
| Soggetto topico |
Lagrange equations
Mathematics Numerical analysis -- Problems, exercises, etc Numerical analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-73097-6
1-118-40746-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Half Title page; Title page; Copyright page; Dedication; Preface; 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; 1.8 Literature Review; References; 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 Problems2.4 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 Examples; 3.9 Fixed-Point Iteration 3.10 Roots of Polynomials, Part 13.11 Special Topics in Root-Finding Methods; 3.12 Very High-Order Methods and the Efficiency Index; 3.13 Literature and Software Discussion; References; 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 Problems4.10 Tension Splines; 4.11 Least Squares Concepts in Approximation; 4.12 Advanced Topics in Interpolation Error; 4.13 Literature and Software Discussion; References; 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; 5.9 Literature and Software Discussion; References Chapter 6: Numerical Methods for Ordinary Differential Equations6.1 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; 6.11 Literature and Software Discussion; References; 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 |
| Record Nr. | UNINA-9910463760403321 |
|
Epperson James F
|
||
| Hoboken, : Wiley, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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