Chapter 1: Mathematical Preliminaries and Error Analysis
1.1 Review of Calculus
1.2 Round-off-Errors and Computer Arithmetic
1.3 Algorithms and Convergence
1.4 Numerical Software

Chapter 2: Solution of Equations in One Variable
2.1 The Bisection Method
2.2 Fixed-Point Iteration
2.3 Newton's Method and Extensions
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

Chapter 3: Interpolation and Polynomial Approximation
3.1 Interpolation and the Lagrange Polynomial
3.2 Data Approximation and Neville's Method
3.3 Divided Differences
3.4 Hermite Interpolation
3.5 Cubic Spline Interpolation
3.6 Parametric Curves
3.7 Survey of Methods and Software

Chapter 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 Impropoer Integrals
4.10 Survey of Methods and Software

Chapter 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 Multistep Methods
5.7 Variable Step-Size Multistep 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

Chapter 6: Direct Methods for Solving Linear Systems
6.1 Linear Systems of Equations
6.2 Pivoting Strategies
6.3 Linear Algebra and Matrix Inversion
6.4 The Determinant of Matrix
6.5 Matrix Factorization
6.6 Special Types of Matrices
6.7 Survey of Methods and Software

Chapter 7: Iterative Techniques in Matrix Algebra
7.1 Norms of Vectors and Matrices
7.2 Eigenvalues and Eigenvectors
7.3 The Jacobi and Gauss-Siedel Iterative Techniques
7.4 Relaxation Techniques for Solving Linear Systems
7.5 Error Bounds and Iterative Refinement
7.6 The Conjugate Gradient Method
7.7 Survey of Methods and Software

Chapter 8: Approximation Theory
8.1 Discrete Least Squares Approximation
8.2 Orthogonal Polynomials and Least Squares Approximation
8.3 Chebyshev Polynomials and Economization of Power Series
8.4 Rational Function Approximation
8.5 Trigonometric Polynomial Approximation
8.6 Fast Fourier Transforms
8.7 Survey of Methods and Software

Chapter 9: Approximating Eigenvalues
9.1 Linear Algebra and Eigenvalues
9.2 Orthogonal Matrices and Similarity Transformation
9.3 The Power Method
9.4 Householder's Method
9.5 The QR Algorithm
9.6 Singular Value Decomposition
9.7 Survey of Methods and Software

Chapter 10: Numerical Solutions of Nonlinear Systems of Equations
10.1 Fixed Points for Functions of Several Variables
10.2 Newton's Method
10.3 Quasi-Newton Methods
10.4 Steepest Descent Techniques
10.5 Homotopy and Continuation Methods
10.6 Survey of Methods and Software

Chapter 11: Boundary-Value Problems for Ordinary Differential Equations
11.1 The Linear Shooting Method
11.2 The Shooting Method for Nonlinear Problems
11.3 Finite-Difference Methods for Linear Problems
11.4 Finite-Difference Methods for Nonlinear Problems
11.5 The Rayleigh-Ritz Method
11.6 Survey of Methods and Software

Chapter 12: Numerical Solutions to Partial Differential Equations
12.1 Elliptic Partial Differential Equations
12.2 Parabolic Partial Differential Equations
12.3 Hyperbolic Partial Differential Equations
12.4 An Introduction to the Finite-Element Method
12.5 Survey of Methods and Software