Topics of Numerical Methods

Introduction

Introduction
Measuring Errors

Sources of Error

Binary Representation

Floating Pt Representation

Propagation of Errors

Taylor Theorem Revisit

Differentiation

Primer on Differentiation
Continuous Function

Discrete Function

Nonlinear Equations

Quadratic Equations
Cubic Equations

Bisection Method

Newton-Raphson Method

Secant Method

False-Position Method

Simultaneous Linear Equations

Intro to Matrix Algebra
Gaussian Elimination

Gauss-Seidel Method

LU Decomposition

Cholesky and LDL Decomposition

Interpolation

Background of Interpolation
Direct Method

Newton’s Dif Method

Lagrange Method

Spline Method

Regression

Primer on Regression
Linear Regression

Nonlinear Regression

Adequacy of Regression

Integration

Primer on Integral Calculus
Trapezoidal Rule

Simpson’s 1/3rd Rule

Romberg Integration

Gauss-Quad Rule

Discrete Data Integration

Improper Integration

Simpson’s 3/8 Rule

Ordinary Differential Equations

Primer on Ordinary Differential Equations
Euler’s Method

Runge-Kutta 2nd

Runge-Kutta 4th

Finite Diff Method

Shooting Method

Higher Order/Coupled

Optimization

Golden Section Search Method
Newton’s Method

Multidimensional Direct Search Method

Multidimensional Gradient Method
Simplex Method

Partial Differential Equations

Introduction to Partial Differential Equations

Parabolic Partial Differential Equations
Elliptic Partial Differential Equations

Finite Element Methods

 

Fast Fourier Transforms

Introduction to Fourier Series

Continuous Fourier Series

Fast Transform Pair

Informal Development of Fast Transform Pair