Bisection Method

Fixed Point Iteration

Newton Method

Error Analysis for Iterative Methods and Modified Newton

Newton Method for Nonlinear Systems and Optimization

Muller's Method

Interpolation and the Lagrange Polynomials

Data Approximation and Neville's Method

Divided Differences

Errors in Polynomial Interpolation

Hermite Interpolation

Spline Interpolation

Bezier Curves

Least Squares Approximation

Orthogonal Polynomials and Least Squares Approximation

Numerical Differentiation. Finite Difference Approximations

Derivation of Numerical Differentiation Formulas

Numerical Integration

Newton-Cotes Formulas

Composite Numerical Integration

Adaptive Simpson

Gauss Quadrature

Multiple Integration

Gauss Quadrature in 2D

Direct Solution of Linear Systems

Pivot Strategies. Counting Operations

LU Factorization

Tridiagonal Algorithm

Special Type of Matrices

Matrix Norms

Eigenvalues and Eigenvectors

Iterative Methods for Linear Systems

A 3x3 example of Iterative Methods for Linear Systems

Convergence Theorems for Iterative Methods for Linear Systems