Numerical Methods Course

Videos listed in chronological order

Mathematical Modeling, role of numerical methods, and errors in numerical approximations.

• mathematical modeling
• falling parachutist example
• numerical error
• taylor series
• finite difference approximations and order of error

Introduction to programming in Matlab.

• introduction to matlab
• matlab functions and conditional branching
• more on matlab functions and intro to loops
• for loops and riemann sums
• matlab arrays
• riemann sum integrate example using arrays
• basic 2D plotting in matlab

Numerical Methods for finding roots of equations.

• intro to roots of equations
• bracketing methods: the bisection method
• bracketing methods: the false position method
• bisection code in matlab
• intro to open methods and the Newton-Raphson algorithm
• the secant method for finding roots
• detecting convergence in root finding methods

Matrix Methods for solving linear and non-linear sets of equations.

• basic matrix multiplication
• putting sets of linear equations into matrix form
• introduction to matrix methods
• using the matrix inverse to solve the Ax=b problem
• calculating the matrix inverse in matlab and excel
• elimination methods: gaussian and gauss-jordan elimination
• turning matrix algorithms into code
• solving sets of non-linear equations
• solving sets of non-linear equations in Matlab

Optimization: 1-D unconstrained, multi-dimensional, and constrained

• introduction to the basic ideas of optimization in engineering
• introduction to 1D unconstrained optimization
• golden-section search algorithm
• golden-section search by hand
• intro to multi-dimensional optimization with gradient descent

Curve Fitting and Interpolation

• conceptual intro to curve fitting
• intro to least-squares regression
• basic stats for doing regression
• spreadsheet example of linear regression
• linearization of nonlinear relationships

Ordinary Differential Equations

• transforming from nth-order ODE to system of n 1st-order ODEs
• solving system of ODEs in Matlab