1. MATHEMATICAL PRELIMINARIES
1.1 Review of Calculus
1.2 Round-off Errors and Computer Arithmetic
1.3 Algorithms and Convergence
1.4 Numerical Software
2. SOLUTIONS OF EQUATIONS IN ONE VARIABLE
2.1 The Bisection Method
2.2 Fixed-Point Iteration
2.3 The Newton's Method
2.4 Error Analysis for Iterative Methods
2.5 Accelerating Convergence
2.6 Zeros of Polynomials and Muller's Method
2.7 Survey of Methods and Software
3. INTERPOLATION AND POLYNOMIAL APPROXIMATION
3.1 Interpolation and the LaGrange Polynomial
3.2 Divided Differences
3.3 Hermite Interpolation
3.4 Cubic Spline Interpolation
3.5 Parametric Curves
3.6 Survey of Methods and Software
4. NUMERICAL DIFFERENTIATION AND INTEGRATION
4.1 Numerical Differentiation
4.2 Richardson's Extrapolation
4.3 Elements of Numerical Integration
4.4 Composite Numerical Integration
4.5 Romberg Integration
4.6 Adaptive Quadrature Methods
4.7 Gaussian Quadrature
4.8 Multiple Integrals
4.9 Improper Integrals
4.10 Survey of Methods and Software
5. INITIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
5.1 The Elementary Theory of Initial-Value Problems
5.2 Euler's Method
5.3 Higher-Order Taylor Methods
5.4 Runge-Kutta Methods
5.5 Error Control and the Runge-Kutta-Fehlberg Method
5.6 Multi-Step Methods
5.7 Variable Step-Size Multi-Step Methods
5.8 Extrapolation Methods
5.9 Higher-Order Equations and Systems of Differential Equations
5.10 Stability
5.11 Stiff Differential Equations
5.12 Survey of Methods and Software
6. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS
7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA
8. APPROXIMATION THEORY
9. APPROXIMATING EIGENVALUES
10. NUMERICAL SOLUTIONS OF NONLINEAR SYSTEMS OF EQUATIONS
11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
12. NUMERICAL SOLUTIONS TO PARTIAL DIFFERENTIAL EQUATIONS
BIBLIOGRAPHY
ANSWERS TO SELECTED EXERCISES
INDEX
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