Lecture 1 - Introduction, Why and how we need computers

Lecture 2 - Representing Arrays and functions on computers

Lecture 3 - Representing functions - Box functions

Lecture 4 - Representing functions - Polynomials and Hat functions

Lecture 5 - Hat functions, Quadratic and Cubic representations

Lecture 6 - Demo - Hat functions, Aliasing

Lecture 7 - Representing Derivatives - finite differences

Lecture 8 - Finite differences, Laplace equation

Lecture 9 - Laplace equation - Jacobi iterations

Lecture 10 - Laplace equation - Iteration matrices

Lecture 11 - Laplace equation - convergence rate

Lecture 12 - Laplace equation - convergence rate Continued

Lecture 13 - Demo - representation error, Laplace equation

Lecture 14 - Demo - Laplace equation, SOR

Lecture 15 - Laplace equation - final, Linear Wave equation

Lecture 16 - Linear wave equation - Closed form and numerical solution, stability analysis

Lecture 17 - Generating a stable scheme and Boundary conditions

Lecture 18 - Modified equation

Lecture 19 - Effect of higher derivative terms on Wave equation

Lecture 20 - Artificial dissipation, upwinding, generating schemes

Lecture 21 - Demo - Modified equation, Wave equation

Lecture 22 - Demo - Wave equation / Heat Equation

Lecture 23 - Quasi-linear One-Dimensional. wave equation

Lecture 24 - Shock speed, stability analysis, Derive Governing equations

Lecture 25 - One-Dimensional Euler equations - Attempts to decouple

Lecture 26 - Derive Eigenvectors, Writing Programs

Lecture 27 - Applying Boundary conditions

Lecture 28 - Implicit Boundary conditions

Lecture 29 - Flux Vector Splitting, setup froms averaging

Lecture 30 - Roes averaging

Lecture 31 - Demo - One Dimensional flow

Lecture 32 - Accelerating convergence - Preconditioning, dual time stepping

Lecture 33 - Accelerating convergence - Intro to Multigrid method

Lecture 34 - Multigrid method

Lecture 35 - Multigrid method - final, Parallel Computing

Lecture 36 - Calculus of Variations - Three Lemmas and a Theorem

Lecture 37 - Calculus of Variations - Application to Laplace Equation

Lecture 38 - Calculus of Variations - Final and Random Walk

Lecture 39 - Overview and Recap of the course