05221nam 22006373u 450 991078762790332120230912141923.01-118-73097-61-118-40746-6(CKB)2670000000501196(EBL)1584988(Au-PeEL)EBL5185089(CaPaEBR)ebr11481410(OCoLC)844790174(CaSebORM)9781118407462(MiAaPQ)EBC1584988(MiAaPQ)EBC5185089(MiAaPQ)EBC7104003(PPN)195538897(EXLCZ)99267000000050119620140106d2013|||| u|| |engur|n|---|||||txtrdacontentcrdamediacrrdacarrierAn Introduction to Numerical Methods and Analysis, Second Edition[electronic resource]2nd ed.Hoboken Wiley20131 online resource (1171 p.)Description based upon print version of record.1-118-36759-6 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 Derivative2.3 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 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 Splines4.9 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; ReferencesChapter 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 Counts7.4 The LU FactorizationPraise 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 tLagrange equationsMathematicsNumerical analysisProblems, exercises, etcNumerical analysisLagrange equations.Mathematics.Numerical analysisNumerical analysis.535.278Epperson James F148399AU-PeELAU-PeELAU-PeELBOOK9910787627903321An Introduction to Numerical Methods and Analysis, Second Edition3703170UNINA