{"product_id":"an-introduction-to-numerical-methods-and-analysis-solutions-manual-paperback-softback-9781118395134","title":"An Introduction to Numerical Methods and Analysis, Solutions Manual (Paperback \/ softback) 9781118395134","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAn Introduction to Numerical Methods and Analysis, Solutions Manual\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eJames F. Epperson (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781118395134, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 10 December 2013\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e316 pages\u003cbr\u003e23.1 x 15.8 x 1.8 cm, 0.445 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eA solutions manual to accompany \u003ci\u003eAn Introduction to Numerical Methods and Analysis, Second Edition\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eAn Introduction to Numerical Methods and Analysis, Second Edition\u003c\/i\u003e 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 \u003ci\u003eSecond Edition\u003c\/i\u003e also features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eChapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material\u003c\/li\u003e \u003cli\u003eExercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises\u003c\/li\u003e \u003cli\u003eWidespread exposure and utilization of MATLAB\u003c\/li\u003e \u003cli\u003eAn appendix that contains proofs of various theorems and other material\u003c\/li\u003e \u003c\/ul\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003e1 Introductory Concepts and Calculus Review 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Basic Tools of Calculus 1\u003c\/p\u003e \u003cp\u003e1.2 Error, Approximate Equality, and Asymptotic Order Notation 12\u003c\/p\u003e \u003cp\u003e1.3 A Primer on Computer Arithmetic 15\u003c\/p\u003e \u003cp\u003e1.4 A Word on Computer Languages and Software 19\u003c\/p\u003e \u003cp\u003e1.5 Simple Approximations 19\u003c\/p\u003e \u003cp\u003e1.6 Application: Approximating the Natural Logarithm 22\u003c\/p\u003e \u003cp\u003e1.7 A Brief History of Computing 25\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 A Survey of Simple Methods and Tools 27\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Horner’s Rule and Nested Multiplication 27\u003c\/p\u003e \u003cp\u003e2.2 Difference Approximations to the Derivative 30\u003c\/p\u003e \u003cp\u003e2.3 Application: Euler’s Method for Initial Value Problems 40\u003c\/p\u003e \u003cp\u003e2.4 Linear Interpolation 44\u003c\/p\u003e \u003cp\u003e2.5 Application— The Trapezoid Rule 48\u003c\/p\u003e \u003cp\u003e2.6 Solution of Tridiagonal Linear Systems 56\u003c\/p\u003e \u003cp\u003e2.7 Application: Simple Two-Point Boundary Value Problems 61\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Root-Finding 65\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Bisection Method 65\u003c\/p\u003e \u003cp\u003e3.2 Newton’s Method: Derivation and Examples 69\u003c\/p\u003e \u003cp\u003e3.3 How to Stop Newton’s Method 73\u003c\/p\u003e \u003cp\u003e3.4 Application: Division Using Newton’s Method 77\u003c\/p\u003e \u003cp\u003e3.5 The Newton Error Formula 81\u003c\/p\u003e \u003cp\u003e3.6 Newton’s Method: Theory and Convergence 84\u003c\/p\u003e \u003cp\u003e3.7 Application: Computation of the Square Root 88\u003c\/p\u003e \u003cp\u003e3.8 The Secant Method: Derivation and Examples 92\u003c\/p\u003e \u003cp\u003e3.9 Fixed Point Iteration 96\u003c\/p\u003e \u003cp\u003e3.10 Roots of Polynomials (Part 1) 99\u003c\/p\u003e \u003cp\u003e3.11 Special Topics in Root-finding Methods 102\u003c\/p\u003e \u003cp\u003e3.12 Very High-order Methods and the Efficiency Index 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Interpolation and Approximation 117\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Lagrange Interpolation 117\u003c\/p\u003e \u003cp\u003e4.2 Newton Interpolation and Divided Differences 120\u003c\/p\u003e \u003cp\u003e4.3 Interpolation Error 132\u003c\/p\u003e \u003cp\u003e4.4 Application: Muller’s Method and Inverse Quadratic Interpolation 139\u003c\/p\u003e \u003cp\u003e4.5 Application: More Approximations to the Derivative 141\u003c\/p\u003e \u003cp\u003e4.6 Hermite Interpolation 142\u003c\/p\u003e \u003cp\u003e4.7 Piecewise Polynomial Interpolation 145\u003c\/p\u003e \u003cp\u003e4.8 An Introduction to Splines 149\u003c\/p\u003e \u003cp\u003e4.9 Application: Solution of Boundary Value Problems 156\u003c\/p\u003e \u003cp\u003e4.10 Tension Splines 159\u003c\/p\u003e \u003cp\u003e4.11 Least Squares Concepts in Approximation 160\u003c\/p\u003e \u003cp\u003e4.12 Advanced Topics in Interpolation Error 166\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Numerical Integration 171\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 A Review of the Definite Integral 171\u003c\/p\u003e \u003cp\u003e5.2 Improving the Trapezoid Rule 173\u003c\/p\u003e \u003cp\u003e5.3 Simpson’s Rule and Degree of Precision 177\u003c\/p\u003e \u003cp\u003e5.4 The Midpoint Rule 187\u003c\/p\u003e \u003cp\u003e5.5 Application: Stirling’s Formula 190\u003c\/p\u003e \u003cp\u003e5.6 Gaussian Quadrature 192\u003c\/p\u003e \u003cp\u003e5.7 Extrapolation Methods 199\u003c\/p\u003e \u003cp\u003e5.8 Special Topics in Numerical Integration 203\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Numerical Methods for Ordinary Differential Equations 211\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 The Initial Value Problem — Background 211\u003c\/p\u003e \u003cp\u003e6.2 Euler’s Method 213\u003c\/p\u003e \u003cp\u003e6.3 Analysis of Euler’s Method 216\u003c\/p\u003e \u003cp\u003e6.4 Variants of Euler’s Method 217\u003c\/p\u003e \u003cp\u003e6.5 Single Step Methods— Runge-Kutta 225\u003c\/p\u003e \u003cp\u003e6.6 Multistep Methods 228\u003c\/p\u003e \u003cp\u003e6.7 Stability Issues 234\u003c\/p\u003e \u003cp\u003e6.8 Application to Systems of Equations 235\u003c\/p\u003e \u003cp\u003e6.9 Adaptive Solvers 240\u003c\/p\u003e \u003cp\u003e6.10 Boundary Value Problems 243\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Numerical Methods for the Solution of Systems of Equations 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Linear Algebra Review 247\u003c\/p\u003e \u003cp\u003e7.2 Linear Systems and Gaussian Elimination 248\u003c\/p\u003e \u003cp\u003e7.3 Operation Counts 254\u003c\/p\u003e \u003cp\u003e7.4 The LU Factorization 256\u003c\/p\u003e \u003cp\u003e7.5 Perturbation, Conditioning and Stability 262\u003c\/p\u003e \u003cp\u003e7.6 SPD Matrices and the Cholesky Decomposition 269\u003c\/p\u003e \u003cp\u003e7.7 Iterative Methods for Linear Systems – A Brief Survey 271\u003c\/p\u003e \u003cp\u003e7.8 Nonlinear Systems: Newton’s Method and Related Ideas 273\u003c\/p\u003e \u003cp\u003e7.9 Application: Numerical Solution of Nonlinear BVP’s 275\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Approximate Solution of the Algebraic Eigenvalue Problem 277\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Eigenvalue Review 277\u003c\/p\u003e \u003cp\u003e8.2 Reduction to Hessenberg Form 280\u003c\/p\u003e \u003cp\u003e8.3 Power Methods 281\u003c\/p\u003e \u003cp\u003e8.4 An Overview of the QR Iteration 284\u003c\/p\u003e \u003cp\u003e8.5 Application: Roots of Polynomials, II 288\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 A Survey of Numerical Methods for Partial Differential Equations 289\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Difference Methods for the Diffusion Equation 289\u003c\/p\u003e \u003cp\u003e9.2 Finite Element Methods for the Diffusion Equation 293\u003c\/p\u003e \u003cp\u003e9.3 Difference Methods for Poisson Equations 294\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 An Introduction to Spectral Methods 299\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Spectral Methods for Two-Point Boundary Value Problems 299\u003c\/p\u003e \u003cp\u003e10.2 Spectral Methods for Time-Dependent Problems 301\u003c\/p\u003e \u003cp\u003e10.3 Clenshaw-Curtis Quadrature 303\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand 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