Solutions manual to accompany an introduction to numerical methods and analysis
A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Third Edition An Introduction to Numerical Methods and Analysis helps students gain a solid understanding of a wide range of numerical approximation methods for solving problems of mathematical analysis. Designed for...
| Otros Autores: | |
|---|---|
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Hoboken, New Jersey :
Wiley
[2021]
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| Edición: | Third edition |
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009645691906719 |
Tabla de Contenidos:
- <P><b>1 Introductory Concepts and Calculus Review 1</b></p> <p>1.1 Basic Tools of Calculus 1</p> <p>1.2 Error, Approximate Equality, and Asymptotic Order Notation 10</p> <p>1.3 A Primer on Computer Arithmetic 13</p> <p>1.4 A Word on Computer Languages and Software 17</p> <p>1.5 A Brief History of Scientific Computing 18</p> <p><b>2 A Survey of Simple Methods and Tools 19</b></p> <p>2.1 Horner's Rule and Nested Multiplication 19</p> <p>2.2 Difference Approximations to the Derivative 22</p> <p>2.3 Application: Euler's Method for Initial Value Problems 30</p> <p>2.4 Linear Interpolation 34</p> <p>2.5 Application-The Trapezoid Rule 38</p> <p>2.6 Solution of Tridiagonal Linear Systems 46</p> <p>2.7 Application: Simple Two-Point Boundary Value Problems 50</p> <p><b>3 Root-Finding 55</b></p> <p>3.1 The Bisection Method 55</p> <p>3.2 Newton's Method: Derivation and Examples 59</p> <p>3.3 How to Stop Newton's Method 63</p> <p>3.4 Application: Division Using Newton's Method 66</p> <p>3.5 The Newton Error Formula 69</p> <p>3.6 Newton's Method: Theory and Convergence 72</p> <p>3.7 Application: Computation of the Square Root 76</p> <p>3.8 The Secant Method: Derivation and Examples 79</p> <p>3.9 Fixed Point Iteration 83</p> <p>3.10 Roots of Polynomials (Part 1) 85</p> <p>3.11 Special Topics in Root-finding Methods 88</p> <p>3.12 Very High-order Methods and the Efficiency Index 98</p> <p><b>4 Interpolation and Approximation 101</b></p> <p>4.1 Lagrange Interpolation 101</p> <p>4.2 Newton Interpolation and Divided Differences 104</p> <p>4.3 Interpolation Error 114</p> <p>4.4 Application: Muller's Method and Inverse Quadratic Interpolation 119</p> <p>4.5 Application: More Approximations to the Derivative 121</p> <p>4.6 Hermite Interpolation 122</p> <p>4.7 Piecewise Polynomial Interpolation 125</p> <p>4.8 An Introduction to Splines 129</p> <p>4.9 Tension Splines 135</p> <p>4.10 Least Squares Concepts in Approximation 137</p> <p>4.11 Advanced Topics in Interpolation Error 142</p> <p><b>5 Numerical Integration 149</b></p> <p>5.1 A Review of the Definite Integral 149</p> <p>5.2 Improving the Trapezoid Rule 151</p> <p>5.3 Simpson's Rule and Degree of Precision 154</p> <p>5.4 The Midpoint Rule 162</p> <p>5.5 Application: Stirling's Formula 166</p> <p>5.6 Gaussian Quadrature 167</p> <p>5.7 Extrapolation Methods 173</p> <p>5.8 Special Topics in Numerical Integration 177</p> <p><b>6 Numerical Methods for Ordinary Differential Equations 185</b></p> <p>6.1 The Initial Value Problem-Background 185</p> <p>6.2 Euler's Method 187</p> <p>6.3 Analysis of Euler's Method 189</p> <p>6.4 Variants of Euler's Method 190</p> <p>6.5 Single Step Methods-Runge-Kutta 197</p> <p>6.6 Multistep Methods 200</p> <p>6.7 Stability Issues 204</p> <p>6.8 Application to Systems of Equations 206</p> <p>6.9 Adaptive Solvers 210</p> <p>6.10 Boundary Value Problems 212</p> <p><b>7 Numerical Methods for the Solution of Systems of Equations 217</b></p> <p>7.1 Linear Algebra Review 217</p> <p>7.2 Linear Systems and Gaussian Elimination 218</p> <p>7.3 Operation Counts 223</p> <p>7.4 The <i>LU </i>Factorization 224</p> <p>7.5 Perturbation, Conditioning and Stability 229</p> <p>7.6 SPD Matrices and the Cholesky Decomposition 235</p> <p>7.7 Application: Numerical Solution of Linear Least Squares Problems 236</p> <p>7.8 Sparse and Structured Matrices 240</p> <p>7.9 Iterative Methods for Linear Systems
- A Brief Survey 241</p> <p>7.10 Nonlinear Systems: Newton's Method and Related Ideas 242</p> <p>7.11 Application: Numerical Solution of Nonlinear BVP's 244</p> <p><b>8 Approximate Solution of the Algebraic Eigenvalue Problem 247</b></p> <p>8.1 Eigenvalue Review 247</p> <p>8.2 Reduction to Hessenberg Form 249</p> <p>8.3 Power Methods 250</p> <p>8.4 Bisection and Inertia to Compute Eigenvalues of Symmetric Matrices 253</p> <p>8.5 An Overview of the <i>QR </i>Iteration 257</p> <p>8.6 Application: Roots of Polynomials, II 260</p> <p>8.7 Application: Computation of Gaussian Quadrature Rules 261</p> <p><b>9 A Survey of Numerical Methods for Partial Differential Equations 265</b></p> <p>9.1 Difference Methods for the Diffusion Equation 265</p> <p>9.2 Finite Element Methods for the Diffusion Equation 270</p> <p>9.3 Difference Methods for Poisson Equations 271</p> <p><b>10 An Introduction to Spectral Methods 277</b></p> <p>10.1 Spectral Methods for Two-Point Boundary Value Problems 277</p> <p>10.2 Spectral Methods in Two Dimensions 279</p> <p>10.3 Spectral Methods for Time-Dependent Problems 282</p> <p>10.4 Clenshaw-Curtis Quadrature 283</p>
