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Numerical Analysis, 10th Edition Numerical Analysis, 10th Edition
Chapter 1
Mathematical Preliminaries And Error Analysis
| 1-1 | Review of Calculus | Exercises Set | p.11 |
| Discussion Question | p.14 | ||
| 1-2 | Round-off-Errors and Computer Arithmetic | Exercises Set | p.25 |
| Discussion Question | p.29 | ||
| 1-3 | Algorithms and Convergence | Exercises Set | p.35 |
| Discussion Question | p.38 | ||
| 1-4 | Numerical Software | Discussion Question | p.44 |
Chapter 2
Solutions Of Equations In One Variable
| 2-1 | The Bisection Method | Exercises Set | p.53 |
| Discussion Question | p.54 | ||
| 2-2 | Fixed-Point Iteration | Exercises Set | p.63 |
| Discussion Question | p.66 | ||
| 2-3 | Newton's Method and Its Extensions | Exercises Set | p.74 |
| Discussion Question | p.78 | ||
| 2-4 | Error Analysis for Iterative Methods | Exercises Set | p.84 |
| Discussion Question | p.85 | ||
| 2-5 | Accelerating Convergence | Exercises Set | p.89 |
| Discussion Question | p.91 | ||
| 2-6 | Zeros of Polynomials and Muller's Method | Exercises Set | p.99 |
| Discussion Question | p.100 | ||
| 2-7 | Numerical Software and Chapter Review | Discussion Question | p.101 |
Chapter 3
Interpolation And Polynomial Approximation
| 3-1 | Interpolation and the Lagrange Polynomial | Exercises Set | p.112 |
| Discussion Question | p.115 | ||
| 3-2 | Data Approximation and Neville's Method | Exercises Set | p.120 |
| Discussion Question | p.122 | ||
| 3-3 | Divided Differences | Exercises Set | p.130 |
| Discussion Question | p.133 | ||
| 3-4 | Hermite Interpolation | Exercises Set | p.139 |
| Discussion Question | p.141 | ||
| 3-5 | Cubic Spline Interpolation | Exercises Set | p.158 |
| Discussion Question | p.162 | ||
| 3-6 | Parametric Curves | Exercises Set | p.167 |
| Discussion Question | p.168 | ||
| 3-7 | Numerical Software and Chapter Review | Discussion Question | p.169 |
Chapter 4
Numerical Differentiation And Integration
| 4-1 | Numerical Differentiation | Exercises Set | p.180 |
| Discussion Question | p.183 | ||
| 4-2 | Richardson's Extrapolation | Exercises Set | p.189 |
| Discussion Question | p.191 | ||
| 4-3 | Elements of Numerical Integration | Exercises Set | p.200 |
| Discussion Question | p.201 | ||
| 4-4 | Composite Numerical Integration | Exercises Set | p.208 |
| Discussion Question | p.211 | ||
| 4-5 | Romberg Integration | Exercises Set | p.217 |
| Discussion Question | p.219 | ||
| 4-6 | Adaptive Quadrature Methods | Exercises Set | p.226 |
| Discussion Question | p.228 | ||
| 4-7 | Gaussian Quadrature | Exercises Set | p.234 |
| Discussion Question | p.235 | ||
| 4-8 | Multiple Integrals | Exercises Set | p.248 |
| Discussion Question | p.250 | ||
| 4-9 | Improper Integrals | Exercises Set | p.255 |
| Discussion Question | p.256 | ||
| 4-10 | Numerical Software and Chapter Review | Discussion Question | p.257 |
Chapter 5
Initial-Value Problems For Ordinary Differential Equations
| 5-1 | The Elementary Theory of Initial-Value Problems | Exercises Set | p.264 |
| Discussion Question | p.265 | ||
| 5-2 | Euler's Method | Exercises Set | p.272 |
| Discussion Question | p.275 | ||
| 5-3 | Higher-Order Taylor Methods | Exercises Set | p.280 |
| Discussion Question | p.282 | ||
| 5-4 | Runge-Kutta Methods | Exercises Set | p.291 |
| Discussion Question | p.293 | ||
| 5-5 | Error Control and the Runge-Kutta-Fehlberg Method | Exercises Set | p.300 |
| Discussion Question | p.302 | ||
| 5-6 | Multistep Methods | Exercises Set | p.314 |
| Discussion Question | p.316 | ||
| 5-7 | Variable Step-Size Multistep Methods | Exercises Set | p.321 |
| Discussion Question | p.322 | ||
| 5-8 | Extrapolation Methods | Exercises Set | p.329 |
| Discussion Question | p.330 | ||
| 5-9 | Higher-Order Equations and Systems of Differential Equations | Exercises Set | p.337 |
| Discussion Question | p.339 | ||
| 5-10 | Stability | Exercises Set | p.348 |
| Discussion Question | p.349 | ||
| 5-11 | Stiff Differential Equations | Exercises Set | p.355 |
| Discussion Question (5-11) | p.356 | ||
| 5-12 | Numerical Software | Discussion Question (5-12) | p.357 |
Chapter 6
Direct Methods For Solving Linear Systems
| 6-1 | Linear Systems of Equations | Exercises Set | p.371 |
| Discussion Question | p.375 | ||
| 6-2 | Pivoting Strategies | Exercises Set | p.383 |
| Discussion Question | p.385 | ||
| 6-3 | Linear Algebra and Matrix Inversion | Exercises Set | p.394 |
| Discussion Question | p.400 | ||
| 6-4 | The Determinant of a Matrix | Exercises Set | p.403 |
| Discussion Question | p.406 | ||
| 6-5 | Matrix Factorization | Exercises Set | p.413 |
| Discussion Question | p.416 | ||
| 6-6 | Special Types of Matrices | Exercises Set | p.429 |
| Discussion Question (6-6) | p.433 | ||
| 6-7 | Numerical Software | Discussion Question (6-7) | p.433 |
Chapter 7
Iterative Techniques In Matrix Algebra
| 7-1 | Norms of Vectors and Matrices | Exercises Set |
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