MATH4500/6500: Numerical Analysis I

Note 1.1: Review of Calculus (Post)

Note 1.2: Round-off Errors and Computer Arithmetic (Post)

Note 1.3: Algorithms and Convergence (Post)

Note 2.1: The Bisection Method (Post)

Note 2.2: Fixed-Point Iteration (Post)

Note 2.3: Newton’s Method and Its Extensions (Post)

Note 3.1: Interpolating and the Lagrange Polynomial (Post)

Note 3.3: Divided Differences (Post)

Note 3.4: Hermite Interpolation (Post)

Note 3.5: Cubic Spline Interpolation (Post)

Note 4.1: Numerical Differentiation (Post)

Note 4.3: Elements of Numerical Integration (Post)

Note 4.4: Composite Numerical Integration (Post)

Note 4.7: Gaussian Quadrature (Post)

MATLAB Code 1: The Bisection Method / Fixed-Point Iteration

MATLAB Code 2: Newton's Method / The Secant Method

MATLAB Code 3: Interpolating and the Lagrange Polynomial / Divided Differences

MATLAB Code 4: Hermite Interpolation / Cubic Spline Interpolation

MATLAB Code 5: Elements of Numerical Integration / Composite Numerical Integration / Gaussian Quadrature

The Jacobi and Gauss-Seidel Iterative Techniques

The Power Method

Finite-Difference Methods for Linear Problems

Finite Difference Methods for Black-Scholes

Euler's and High-Order Taylor Methods

Steepest Descent Techniques

The Conjugate Gradient Method