Sold Out
Book Categories |
Preface | ||
Acknowledgments | ||
Ch. 1 | Introductory Concepts and Calculus Review | 1 |
1.1 | Basic Tools of Calculus | 2 |
1.2 | Error, Approximate Equality, and Asymptotic Order Notation | 14 |
1.3 | A Primer on Computer Arithmetic | 20 |
1.4 | A Word on Computer Languages and Software | 28 |
1.5 | Simple Approximations | 29 |
1.6 | Application: Approximating the Natural Logarithm | 33 |
Ch. 2 | A Survey of Simple Methods and Tools | 37 |
2.1 | Homer's Rule and Nested Multiplication | 37 |
2.2 | Difference Approximations to the Derivative | 40 |
2.3 | Application: Euler's Method for Initial Value Problems | 48 |
2.4 | Linear Interpolation | 53 |
2.5 | Application: The Trapezoid Rule | 60 |
2.6 | Solution of Tridiagonal Linear Systems | 69 |
2.7 | Application: Simple Two-Point Boundary Value Problems | 75 |
Ch. 3 | Root Finding | 80 |
3.1 | The Bisection Method | 81 |
3.2 | Newton's Method: Derivation and Examples | 87 |
3.3 | How to Stop Newton's Method | 93 |
3.4 | Application: Division Using Newton's Method | 96 |
3.5 | The Newton Error Formula | 100 |
3.6 | Newton's Method: Theory and Convergence | 105 |
3.7 | Application: Computation of the Square Root | 109 |
3.8 | The Secant Method: Derivation and Example | 111 |
3.9 | Fixed-Point Iteration | 116 |
3.10 | Special Topics in Root-Finding Methods | 126 |
Ch. 4 | Interpolation and Approximation | 150 |
4.1 | Lagrange Interpolation | 151 |
4.2 | Newton Interpolation and Divided Differences | 156 |
4.3 | Interpolation Error | 166 |
4.4 | Application: Muller's Method and Inverse Quadratic | 170 |
4.5 | Application: More Approximation to the Derivative | 174 |
4.6 | Hermite Interpolation | 177 |
4.7 | Piecewise Polynomial Interpolation | 182 |
4.8 | An Introduction to Splines | 189 |
4.9 | Application: Solution of Boundary Value Problems | 204 |
4.10 | Least Squares Concepts in Approximation | 209 |
4.11 | Advanced Topics in Interpolation Error | 230 |
4.12 | Literature and Software Discussion | 243 |
Ch. 5 | Numerical Integration | 245 |
5.1 | A Review of the Definite Integral | 246 |
5.2 | Improving the Trapezoid Rule | 248 |
5.3 | Simpson's Rule and Degree of Precision | 253 |
5.4 | The Midpoint Rule | 265 |
5.5 | Application: Stirling's Formula | 268 |
5.6 | Gaussian Quadrature | 270 |
5.7 | Extrapolation Methods | 281 |
5.8 | Special Topics in Numerical Integration | 288 |
Ch. 6 | Numerical Methods for Ordinary Differential Equations | 312 |
6.1 | The Initial Value Problem: Background | 313 |
6.2 | Euler's Method | 318 |
6.3 | Analysis of Euler's Method | 322 |
6.4 | Variants of Euler's Method | 326 |
6.5 | Single Step Methods: Runge-Kutta | 343 |
6.6 | Multistep Methods | 350 |
6.7 | Stability Issues | 356 |
6.8 | Application to Systems of Equations | 363 |
6.9 | Adaptive Solvers | 370 |
6.10 | Boundary Value Problems | 383 |
6.11 | Literature and Software Discussion | 392 |
Ch. 7 | Numerical Methods for the Solution of Systems | 394 |
7.1 | Linear Algebra Review | 395 |
7.2 | Linear Systems and Gaussian Elimination | 397 |
7.3 | Operation Counts | 404 |
7.4 | The LU Factorization | 406 |
7.5 | Perturbation, Conditioning, and Stability | 416 |
7.6 | SPD Matrices and the Cholesky Decomposition | 434 |
7.7 | Iterative Methods for Linear Systems: A Brief Survey | 437 |
7.8 | Nonlinear Systems: Newton's Method and Related Ideas | 446 |
7.9 | Application: Numerical Solution of Nonlinear BVPs | 452 |
7.10 | Literature and Software Discussion | 454 |
Ch. 8 | Approximate Solution of the Algebraic Eigenvalue Problem | 456 |
8.1 | Eigenvalue Review | 457 |
8.2 | Reduction to Hessenberg Form | 463 |
8.3 | Power Methods | 471 |
8.4 | An Overview of the QR Iteration | 490 |
Ch. 9 | A Survey of Finite Difference Methods for Partial Differential Equations | 500 |
9.1 | Difference Methods for the Diffusion Equation | 501 |
9.2 | Difference Methods for Poisson Equations | 517 |
App. A | Proofs of Selected Theorems, and other Additional Material | 535 |
App. B | Proofs of Selected Theorems, and other Additional Material | 542 |
Index | 549 |
Login|Complaints|Blog|Games|Digital Media|Souls|Obituary|Contact Us|FAQ
CAN'T FIND WHAT YOU'RE LOOKING FOR? CLICK HERE!!! X
You must be logged in to add to WishlistX
This item is in your Wish ListX
This item is in your CollectionAn Introduction to Numerical Methods and Analysis
X
This Item is in Your InventoryAn Introduction to Numerical Methods and Analysis
X
You must be logged in to review the productsX
X
X
Add An Introduction to Numerical Methods and Analysis, The objective of the book is for the reader to learn where approximation methods come from, why they work, why they sometimes don't work, and when to use which of many techniques that are available, and to do all this in a style that emphasizes readabilit, An Introduction to Numerical Methods and Analysis to the inventory that you are selling on WonderClubX
X
Add An Introduction to Numerical Methods and Analysis, The objective of the book is for the reader to learn where approximation methods come from, why they work, why they sometimes don't work, and when to use which of many techniques that are available, and to do all this in a style that emphasizes readabilit, An Introduction to Numerical Methods and Analysis to your collection on WonderClub |