| 1 | Introduction, Why and how we need computers | PDF unavailable |
| 2 | Representing Arrays and functions on computers | PDF unavailable |
| 3 | Representing functions - Box functions | PDF unavailable |
| 4 | Representing functions - Polynomials & Hat functions | PDF unavailable |
| 5 | Hat functions, Quadratic & Cubic representations | PDF unavailable |
| 6 | Demo - Hat functions, Aliasing | PDF unavailable |
| 7 | Representing Derivatives - finite differences | PDF unavailable |
| 8 | Finite differences, Laplace equation | PDF unavailable |
| 9 | Laplace equation - Jacobi iterations | PDF unavailable |
| 10 | Laplace equation - Iteration matrices | PDF unavailable |
| 11 | Laplace equation - convergence rate | PDF unavailable |
| 12 | Laplace equation - convergence rate Continued | PDF unavailable |
| 13 | Demo - representation error, Laplace equation | PDF unavailable |
| 14 | Demo - Laplace equation, SOR | PDF unavailable |
| 15 | Laplace equation - final, Linear Wave equation | PDF unavailable |
| 16 | Linear wave equation - Closed form & numerical solution, stability analysis | PDF unavailable |
| 17 | Generating a stable scheme & Boundary conditions | PDF unavailable |
| 18 | Modified equation | PDF unavailable |
| 19 | Effect of higher derivative terms on Wave equation | PDF unavailable |
| 20 | Artificial dissipation, upwinding, generating schemes | PDF unavailable |
| 21 | Demo - Modified equation, Wave equation | PDF unavailable |
| 22 | Demo - Wave equation / Heat Equation | PDF unavailable |
| 23 | Quasi-linear One-Dimensional. wave equation | PDF unavailable |
| 24 | Shock speed, stability analysis, Derive Governing equations | PDF unavailable |
| 25 | One-Dimensional Euler equations - Attempts to decouple | PDF unavailable |
| 26 | Derive Eigenvectors, Writing Programs | PDF unavailable |
| 27 | Applying Boundary conditions | PDF unavailable |
| 28 | Implicit Boundary conditions | PDF unavailable |
| 29 | Flux Vector Splitting, setup froms averaging | PDF unavailable |
| 30 | Roes averaging | PDF unavailable |
| 31 | Demo - One Dimensional flow | PDF unavailable |
| 32 | Accelerating convergence - Preconditioning, dual time stepping | PDF unavailable |
| 33 | Accelerating convergence, Intro to Multigrid method | PDF unavailable |
| 34 | Multigrid method | PDF unavailable |
| 35 | Multigrid method - final, Parallel Computing | PDF unavailable |
| 36 | Calculus of Variations - Three Lemmas and a Theorem | PDF unavailable |
| 37 | Calculus of Variations - Application to Laplace Equation | PDF unavailable |
| 38 | Calculus of Variations -final & Random Walk | PDF unavailable |
| 39 | Overview and Recap of the course | PDF unavailable |