An Introduction to Numerical Methods and Analysis
(Sprache: Englisch)
The objective of this book is for the reader to learn where approximation methods come from, why they work, why they sometimes don't work, and when to use which of many techniques that are available, and to do all this in a way that emphasizes readability...
Leider schon ausverkauft
versandkostenfrei
Buch (Gebunden)
99.90 €
- Lastschrift, Kreditkarte, Paypal, Rechnung
- Kostenlose Rücksendung
- Ratenzahlung möglich
Produktdetails
Produktinformationen zu „An Introduction to Numerical Methods and Analysis “
Klappentext zu „An Introduction to Numerical Methods and Analysis “
The objective of this book is for the reader to learn where approximation methods come from, why they work, why they sometimes don't work, and when to use which of many techniques that are available, and to do all this in a way that emphasizes readability and usefulness to the numerical methods novice. Each chapter and each section begins with the basic, elementary material and gradually builds up to more advanced topics. The text begins with a review of the important calculus results, and why and where these ideas play an important role throughout the book. Some of the concepts required for the study of computational mathematics are introduced, and simple approximations using Taylor's Theorem are treated in some depth. The exposition is intended to be lively and "student friendly". Exercises run the gamut from simple hand computations that might be characterized as "starter exercises", to challenging derivations and minor proofs, to programming exercises.
Praise for the First Edition
". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." - Zentrablatt Math
". . . carefully structured with many detailed worked examples . . ." - The Mathematical Gazette
". . . an up-to-date and user-friendly account . . ." - Mathematika
An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics.
A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth.
The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.
". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." - Zentrablatt Math
". . . carefully structured with many detailed worked examples . . ." - The Mathematical Gazette
". . . an up-to-date and user-friendly account . . ." - Mathematika
An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics.
A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth.
The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.
Inhaltsverzeichnis zu „An Introduction to Numerical Methods and Analysis “
PrefaceBR />1. Introductory Concepts and Calculus ReviewBR />
1.1 Basic Tools of CalculusBR />
1.2 Error, Approximate Equality, and Asymptotic Order NotationBR />
1.3 A Primer on Computer ArithmeticBR />
1.4 A Word on Computer Languages and SoftwareBR />
1.5 Simple ApproximationsBR />
1.6 Application: Approximating the Natural LogarithmBR />
ReferencesBR />
2. A Survey of Simple Methods and ToolsBR />
2.1 Horner's Rule and Nested MultiplicationBR />
2.2 Difference Approximations to the DerivativeBR />
2.3 Application: Euler's Method for Initial Value ProblemsBR />
2.4 Linear InterpolationBR />
2.5 Application - The Trapezoid RuleBR />
2.6 Solution of Tridiagonal Linear SystemsBR />
2.7 Application: Simple Two-Point Boundary Value ProblemsBR />
3. Root-FindingBR />
3.1 The Bisection MethodBR />
3.2 Newton's Method: Derivation and ExamplesBR />
3.3 How to Stop Newton's MethodBR />
3.4 Application: Division Using Newton's MethodBR />
3.5 The Newton Error FormulaBR />
3.6 Newton's Method: Theory and ConvergenceBR />
3.7 Application: Computation of the Square RootBR />
3.8 The Secant Method: Derivation and ExamplesBR />
3.9 Fixed Point IterationBR />
3.10 Special Topics in Root-finding MethodsBR />
3.11 Literature and Software Discussion 156BR />
ReferencesBR />
4. Interpolation and ApproximationBR />
4.1 Lagrange InterpolationBR />
4.2 Interpolation and Divided DifferencesBR />
4.3 Interpolation ErrorBR />
4.4 Application: Muller's Method and Inverse Quadratic InterpolationBR />
4.5 Application: More Approximations to the DerivativeBR />
4.6 Hermite InterpolationBR />
4.7 Piecewise Polynomial InterpolationBR />
4.8 An Introduction to SplinesBR />
4.9 Application: Solution of Boundary Value ProblemsBR />
4.10 Least Squares Concepts in ApproximationBR />
4.11 Advanced Topics in Interpolation ErrorBR />
4.12 Literature and Software DiscussionBR />
ReferencesBR />
5. Numerical IntegrationBR />
5.1 A Review of the Definite
... mehr
IntegralBR />
5.2 Improving the Trapezoid RuleBR />
5.3 Simpson's Rule and Degree of PrecisionBR />
5.4 The Midpoint RuleBR />
5.5 Application: Stirling's FormulaBR />
5.6 Gaussian QuadratureBR />
5.7 Extrapolation MethodsBR />
5.8 Special Topics in Numerical IntegrationBR />
5.9 Literature and Software DiscussionBR />
ReferencesBR />
6. Numerical Methods for Ordinary Differential EquationsBR />
6.1 The Initial Value Problem - BackgroundBR />
6.2 Euler's MethodBR />
6.3 Analysis of Euler's MethodBR />
6.4 Variants of Euler's MethodBR />
6.5 Single Step Methods? Runge-KuttaBR />
6.6 Multi-step MethodsBR />
6.7 Stability IssuesBR />
6.8 Application to Systems of EquationsBR />
6.9 Adaptive SolversBR />
6.10 Boundary Value ProblemsBR />
6.11 Literature and Software DiscussionBR />
ReferencesBR />
7. Numerical Methods for the Solution of Systems of EquationsBR />
7.1 Linear Algebra ReviewBR />
7.2 Linear Systems and Gaussian EliminationBR />
7.3 Operation CountsBR />
7.4 The LU FactorizationBR />
7.5 Perturbation, Conditioning and StabilityBR />
7.6 SPD Matrices and the Cholesky DecompositionBR />
7.7 Iterative Methods for Linear Systems - A Brief SurveyBR />
7.8 Nonlinear Systems: Newton's Method and Related IdeasBR />
7.9 Application: Numerical Solution of Nonlinear BVP'sBR />
7.10 Literature and Software DiscussionBR />
ReferencesBR />
8. Approximate Solution of the Algebraic Eigenvalue ProblemBR />
8.1 Eigenvalue ReviewBR />
8.2 Reduction to Hessenberg FormBR />
8.3 Power MethodsBR />
8.4 An Overview of the QR IterationBR />
8.5 Literature and Software DiscussionBR />
ReferencesBR />
9. A Survey of Finite Difference Methods for Partial Differential EquationsBR />
9.1 Difference Methods for the Diffusion EquationBR />
9.2 Difference Methods for Poisson EquationsBR />
9.3 Literature and Software DiscussionBR />
ReferencesBR />
Appendix A: Proofs of Selected Theorems, and Other Additional MaterialBR />
A.1 Proofs of the Interpolation Error TheoremsBR />
A.2 Proof of StabilityBR />
A.3 Stiff Systems of Differential Equations and EigenvaluesBR />
A.4 The Matrix Perturbation TheoremBR />
Index
5.2 Improving the Trapezoid RuleBR />
5.3 Simpson's Rule and Degree of PrecisionBR />
5.4 The Midpoint RuleBR />
5.5 Application: Stirling's FormulaBR />
5.6 Gaussian QuadratureBR />
5.7 Extrapolation MethodsBR />
5.8 Special Topics in Numerical IntegrationBR />
5.9 Literature and Software DiscussionBR />
ReferencesBR />
6. Numerical Methods for Ordinary Differential EquationsBR />
6.1 The Initial Value Problem - BackgroundBR />
6.2 Euler's MethodBR />
6.3 Analysis of Euler's MethodBR />
6.4 Variants of Euler's MethodBR />
6.5 Single Step Methods? Runge-KuttaBR />
6.6 Multi-step MethodsBR />
6.7 Stability IssuesBR />
6.8 Application to Systems of EquationsBR />
6.9 Adaptive SolversBR />
6.10 Boundary Value ProblemsBR />
6.11 Literature and Software DiscussionBR />
ReferencesBR />
7. Numerical Methods for the Solution of Systems of EquationsBR />
7.1 Linear Algebra ReviewBR />
7.2 Linear Systems and Gaussian EliminationBR />
7.3 Operation CountsBR />
7.4 The LU FactorizationBR />
7.5 Perturbation, Conditioning and StabilityBR />
7.6 SPD Matrices and the Cholesky DecompositionBR />
7.7 Iterative Methods for Linear Systems - A Brief SurveyBR />
7.8 Nonlinear Systems: Newton's Method and Related IdeasBR />
7.9 Application: Numerical Solution of Nonlinear BVP'sBR />
7.10 Literature and Software DiscussionBR />
ReferencesBR />
8. Approximate Solution of the Algebraic Eigenvalue ProblemBR />
8.1 Eigenvalue ReviewBR />
8.2 Reduction to Hessenberg FormBR />
8.3 Power MethodsBR />
8.4 An Overview of the QR IterationBR />
8.5 Literature and Software DiscussionBR />
ReferencesBR />
9. A Survey of Finite Difference Methods for Partial Differential EquationsBR />
9.1 Difference Methods for the Diffusion EquationBR />
9.2 Difference Methods for Poisson EquationsBR />
9.3 Literature and Software DiscussionBR />
ReferencesBR />
Appendix A: Proofs of Selected Theorems, and Other Additional MaterialBR />
A.1 Proofs of the Interpolation Error TheoremsBR />
A.2 Proof of StabilityBR />
A.3 Stiff Systems of Differential Equations and EigenvaluesBR />
A.4 The Matrix Perturbation TheoremBR />
Index
... weniger
Autoren-Porträt von James F. Epperson
James F. Epperson, PHD, is Associate Editor of Mathematical Reviews. Dr. Epperson received his PhD from Carnegie Mellon University, and his research interests include the numerical solution of nonlinear evolution equations via finite difference methods, the use of kernel functions to solve evolution equations, and numerical methods in mathematical finance.
Bibliographische Angaben
- Autor: James F. Epperson
- 2007, Rev. ed., 736 Seiten, mit Schwarz-Weiß-Abbildungen, mit Abbildungen, Maße: 24,5 cm, Gebunden, Englisch
- Verlag: Wiley & Sons
- ISBN-10: 0470049634
- ISBN-13: 9780470049631
Sprache:
Englisch
Kommentar zu "An Introduction to Numerical Methods and Analysis"
0 Gebrauchte Artikel zu „An Introduction to Numerical Methods and Analysis“
| Zustand | Preis | Porto | Zahlung | Verkäufer | Rating |
|---|
Schreiben Sie einen Kommentar zu "An Introduction to Numerical Methods and Analysis".
Kommentar verfassen