1.1 Basic Concepts and Taylor's Theorem
1.2 Orders of Convergence and Additional Basic Concepts
1.3 Difference Equations
2.1 Floating-Point Numbers and Roundoff Errors
2.2 Absolute and Relative Errors; Loss of Significance
2.3 Stable and Unstable Computations; Conditioning
3.1 Bisection (Interval Halving) Method
3.2 Newton's Method
3.3 Secant Method
3.4 Fixed Points and Functional Iteration
3.5 Computing Zeros of Polynomials
3.6 Homotopy and Continuation Methods
4.1 Matrix Algebra
4.2 The LU and Cholesky Factorizations
4.3 Pivoting and Constructing an Algorithm
4.4 Norms and the Analysis of Errors
4.5 Neumann Series and Iterative Refinement
4.6 Solution of Equations by Iterative Methods
4.7 Steepest Descent and Conjugate Gradient Methods
4.8 Analysis of Roundoff Error in the Gaussian Algorithm
5.1 Matrix Eigenvalue Problem: Power Method
5.2 Schur's and Gershgorin's Theorems
5.3 Orthogonal Factorizations and Least-Squares Problems
5.4 Singular-Value Decomposition and Pseudoinverses
5.5 The QR-Algorithm of Francis for the Eigenvalue Problem
6.1 Polynomial Interpolation
6.2 Divided Differences
6.3 Hermite Interpolation
6.4 Spline Interpolation
6.5 The B-Splines: Basic Theory
6.6 The B-Splines: Applications
6.7 Taylor Series
6.8 Best Approximation: Least-Squares Theory
6.9 Best Approximation: Chebyshev Theory
6.10 Interpolation in Higher Dimensions
6.11 Continued Fractions
6.12 Trigonometric Interpolation
6.13 Fast Fourier Transform
6.14 Adaptive Approximation
7.1 Numerical Differentiation and Richardson Extrapolation
7.2 Numerical Integration Based on Interpolation
7.3 Gaussian Quadrature
7.4 Romberg Integration
7.5 Adaptive Quadrature
7.6 Sard's Theory of Approximating Functionals
7.7 Bernoulli Polynomials and the Euler-Maclaurin Formula
8.1 The Existence and Uniqueness of Solutions
8.2 Taylor-Series Method
8.3 Runge-Kutta Methods
8.4 Multi-Step Methods
8.5 Local and Global Errors; Stability
8.6 Systems and Higher-Order Ordinary Differential Equations
8.7 Boundary-Value Problems
8.8 Boundary-Value Problems: Shooting Methods
8.9 Boundary-Value Problems: Finite-Difference Methods
8.10 Boundary-Value Problems: Collocation
8.11 Linear Differential Equations
8.12 Stiff Equations
9.1 Parabolic Equations: Explicit Methods
9.2 Parabolic Equations: Implicit Methods
9.3 Problems Without Time Dependence: Finite-Difference Methods
9.4 Problems Without Time Dependence: Galerkin and Ritz Methods
9.5 j First-Order Partial Differential Equations; Characteristic Curves
9.6 Quasi-Linear Second-Order Equations; Characteristics
9.7 Other Methods for Hyperbolic Problems
9.8 Multigrid Method
9.9 Fast Methods for Poisson's Equation
10.1 Convexity and Linear Inequalities
10.2 Linear Inequalities
10.3 Linear Programming
10.4 The Simplex Algorithm
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