Licence:
Course Description:
This graduate-level course is a continuation of Computational Science and Engineering I. Topics include numerical methods; initial-value problems; network flows; and optimization.
Lectures:
Lecture 1 - Difference Methods for Ordinary Differential Equations
Lecture 2 - Finite Differences, Accuracy, Stability, Convergence
Lecture 3 - The One-way Wave Equation and CFL / von Neumann Stability
Lecture 4 - Comparison of Methods for the Wave Equation
Lecture 5 - Second-order Wave Equation (including leapfrog)
Lecture 6 - Wave Profiles, Heat Equation / point source
Lecture 7 - Finite Differences for the Heat Equation
Lecture 8 - Convection-Diffusion / Conservation Laws
Lecture 9 - Conservation Laws / Analysis / Shocks
Lecture 10 - Shocks and Fans from Point Source
Lecture 11 - Level Set Method
Lecture 12 - Matrices in Difference Equations (1D, 2D, 3D)
Lecture 13 - Elimination with Reordering: Sparse Matrices
Lecture 14 - Financial Mathematics / Black-Scholes Equation
Lecture 15 - Iterative Methods and Preconditioners
Lecture 16 - General Methods for Sparse Systems
Lecture 17 - Multigrid Methods
Lecture 18 - Krylov Methods / Multigrid Continued
Lecture 19 - Conjugate Gradient Method
Lecture 20 - Fast Poisson Solver
Lecture 21 - Optimization with constraints
Lecture 22 - Weighted Least Squares
Lecture 23 - Calculus of Variations / Weak Form
Lecture 24 - Error Estimates / Projections
Lecture 25 - Saddle Points / Inf-sup condition
Lecture 26 - Two Squares / Equality Constraint Bu = d
Lecture 27 - Regularization by Penalty Term
Lecture 28 - Linear Programming and Duality
Lecture 29 - Duality Puzzle / Inverse Problem / Integral Equations
Source: http://academicearth.org/courses/mathematical-methods-for-engineers-ii
