NOTE: We are upgrading our eBook operations; please allow up to 1-2 days for delivery of your eBook order.
»
Theory and Applications of Numerical Analysis
 
 

Theory and Applications of Numerical Analysis, 2nd Edition

 
Theory and Applications of Numerical Analysis, 2nd Edition,G. Phillips,Peter Taylor,ISBN9780125535601
 
 
 

Phillips   &   Taylor   

Academic Press

9780125535601

9780080519128

447

229 X 152

Print Book + eBook

USD 113.34
USD 188.90

Buy both together and save 40%

Print Book

Paperback

In Stock

Estimated Delivery Time
USD 95.95

eBook
eBook Overview

DRM Free included formats: PDF

USD 92.95
Add to Cart
 
 

Key Features


@bul:* a unique blend of theory and applications
* two brand new chapters on eigenvalues and splines
* inclusion of formal algorithms
* numerous fully worked examples
* a large number of problems, many with solutions

Description

This text is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.

Readership

Advanced undergraduate students in math, computer science, engineering and physical sciences

G. Phillips

George M. Phillips is Reader in Mathematics at the University of St. Andrews, UK. His longstanding collaboration in mathematics has encompassed both teaching and research. Both authors have published many papers in numerical analysis and approximation theory.

Affiliations and Expertise

University of St. Andrews

Peter Taylor

Peter J. Taylor is a retired Senior Lecturer from the University of Strathclyde, UK. His longstanding collaboration in mathematics has encompassed both teaching and research. Both authors have published many papers in numerical analysis and approximation theory.

Affiliations and Expertise

University of Strathclyde, UK

Theory and Applications of Numerical Analysis, 2nd Edition

(Chapter Heading): Introduction. Basic Analysis. Taylors Polynomial and Series. The Interpolating Polynomial. Best Approximation. Splines and Other Approximations. Numerical Integration and Differentiation. Solution of Algebraic Equations of One Variable. Linear Equations. Matrix Norms and Applications. Matrix Eigenvalues and Eigenvectors. Systems of Non-linear Equations. Ordinary Differential Equations. Boundary Value and Other Methods for Ordinary Differential Equations. Appendices. Solutions to Selected Problems. References. Subject Index.

Introduction: What is Numerical Analysis? Numerical Algorithms. Properly Posed and Well-Conditioned Problems. Basic Analysis: Functions. Limits and Derivatives. Sequences and Series. Integration. Logarithmic and Exponential Functions. Taylor's Polynomial and Series: Function Approximation. Taylor's Theorem. Convergence of Taylor Series. Taylor Series in Two Variables. Power Series. The Interpolating Polyomial: Linear Interpolation. Polynomial Interpolation. Accuracy of Interpolation. The Neville–Aitken Algorithm. Inverse Interpolation. Divided Differences. Equally Spaced Points. Derivatives and Differences. Effect of Rounding Error. Choice of Interpolation Points. Examples of Bernstein and Runge. "Best"Approximation: Norms of Functions. Best Approximations. Least Squares Approximations. Orthogonal Functions. Orthogonal Polynomials. Minimax Approximation. Chebyshev Series. Economization of Power Series. The Remez Algorithms. Further Results on Minimax Approximation.Splines and Other Approximations: Introduction. B-Splines. Equally-Spaced Knots. Hermite Interpolation. Pade and Rational Approximation. Numerical Integration and Differentiation: Numerical Integration. Romberg Integration. Gaussian Integration. Indefinite Integrals. Improper Integrals. Multiple Integrals. Numerical Differentiation. Effect of Errors. Solution of Algebraic Equations of One Variable: Introduction. The Bisection Method. Interpolation Methods. One-Point Iterative Methods. Faster Convergence. Higher Order Processes. The Contraction Mapping Theorem. Linear Equations: Introduction. Matrices. Linear Equations. Pivoting. Analysis of Elimination Method. Matrix Factorization. Compact Elimination Methods. Symmetric Matrices. Tridiagonal Matrices. Rounding Errors in Solving Linear Equations. Matrix Norms and Applications: Determinants, Eigenvalues, and Eigenvectors. Vector Norms. Matrix Norms. Conditioning. Iterative Correction from Residual Vectors. Iterative Methods. Matrix Eigenvalues and Eigenvectors: Relations Between Matrix Norms and Eigenvalues; Gerschgorin Theorems. Simple and Inverse Iterative Method. Sturm Sequence Method. The QR Algorithm. Reduction to Tridiagonal Form: Householder's Method. Systems ofNon-Linear Equations: Contraction Mapping Theorem. Newton's Method. Ordinary Differential Equations: Introduction. Difference Equations and Inequalities. One-Step Methods. Truncation Errors of One-Step Methods. Convergence of One-Step Methods. Effect of Rounding Errors on One-Step Methods. Methods Based on Numerical Integration; Explicit Methods. Methods Based on Numerical Integration; Implicit Methods. Iterating with the Corrector. Milne's Method of Estimating Truncation Errors. Numerical Stability. Systems and Higher Order Equations. Comparison of Step-by-Step Methods. Boundary Value and Other Methods for Ordinary Differential Equations: Shooting Method for Boundary Value Problems. Boundary Value Problem. Extrapolation to the Limit. Deferred Correction. Chebyshev Series Method. Appendices. Solutions to Selected Problems. References. Subject Index.

Quotes and reviews

@qu:The first edition was an outstanding work, and the additions that have been put in the Second Edition are very appropriate and have been written up in exemplary fashion.
@source:--Philip J. Davis
 
 
Discount on Science and Technology eBooks | Use code DRMFREE
NOTE: We are upgrading our eBook operations; please allow up to 1-2 days for delivery of your eBook order.