1.1 Preliminary Remarks
1.2 Review of Taylor Series
2.1 Floating-Point Representation
2.2 Loss of Significance
3.1 Bisection Method
3.2 Newton's Method
3.3 Secant Method
4.1 Polynomial Interpolation
4.2 Errors in Polynomial Interpolation
4.3 Estimating Derivatives and Richardson Extrapolation
5.1 Lower and Upper Sums
5.2 Trapezoid Rule
5.3 Romberg Algorithm
6.1 Simpson's Rule and Adaptive Simpson's Rule
6.2 Gaussian Quadrature Formulas
7.1 Naive Gaussian Elimination
7.2 Gaussian Elimination with Scaled Partial Pivoting
7.3 Tridiagonal and Banded Systems
8.1 Matrix Factorizations
8.2 Iterative Solution of Linear Systems
8.3 Eigenvalues and Eigenvectors
8.4 Power Methods
9.1 First-Degree and Second-Degree Splines
9.2 Natural Cubic Splines
9.3 B Splines: Interpolation and Approximation
10.1 Taylor Series Methods
10.2 Runge-Kutta Methods
10.3 Stability, Adaptive Runge-Kutta Methods, and Multistep Methods
11.1 Methods for First-Order Systems
11.2 Higher-Order Equations and Systems
11.3 Adams-Bashforth-Moulton Methods
12.1 Method of Least Squares
12.2 Orthogonal Systems and Chebyshev Polynomials
12.3 Other Examples of the Least Squares Principle
13.1 Random Numbers
13.2 Estimation of Areas and Volumes by Monte Carlo Techniques
13.3 Simulation
14.1 Shooting Method
14.2 A Discretization Method
15.0 Some Partial Differential Equations from Applied Problems
15.1 Parabolic Problems
15.2 Hyperbolic Problems
15.3 Elliptic Problems
16.1 One-Variable Case
16.2 Multivariate Case
17.1 Standard Forms and Duality
17.2 Simplex Method
17.3 Approximate Solution of Inconsistent Linear Systems
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