An Introduction to Numerical Methods and Analysis

Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises."-Zentralblatt MATH ". . . carefully structured with many detailed worked examples."-The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. 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 the Second Edition also features: Chapters and sections that begin with 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 The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.

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 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 Meth…