1. Preliminaries

1.1 ReviewofCalculus

1.2 Binary Numbers

1.3 ErrorAnalysis

2. The Solution of Nonlinear Equations f(x)=0

2.1 Iteration for Solving x=g(x)

2.2 Bracketing Methods for Locating a Root

2.3 Newton-Raphson and Secant Methods

3. The Solution ofLinear Systems AX=B

3.1 Upper-Triangular Linear Systems

3.2 Gaussian Elimination and Pivoting

3.3 Triangular Factorization

3.4 Iterative Methods for Linear Systems

4. Interpolation and Polynomial Approximation

4.1 Taylor Series and Calculation of Functions

4.2 Introduction to Interpolation

4.3 Lagrange Approximation

4.4 Newton Polynomials

5. Curve Fitting

5.1 Least-squares Line

5.2 Curve Fitting

5.3 Interpolation by Spline Functions

5.4 Fourier Seriesand Trigonometric Polynomials

6. Numerical Differentiation

6.1 Approximating The Derivative

6.2 Numerical Differentiation Formulas

7. Numerical Integration

7.1 Introduction to Quadrature

7.2 Composite Trapezoidal and Simpson's Rule

7.3 Recursive Rules and Romberg Integration

7.4 Adaptive Quadrature

8. Eigenvalues and Eigenvectors

8.1 Homogeneous Systems: The Eigenvalue Problem

8.2 Power Method

8.3 Jacobi's Method

8.4 Eigenvalues of Symmetric Matrices