Mathematical Methods for Engineers II

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

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   Lecture 1 - Difference Methods for Ordinary Differential Equations

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   Lecture 2 - Finite Differences, Accuracy, Stability, Convergence

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   Lecture 3 - The One-way Wave Equation and CFL / von Neumann Stability

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   Lecture 4 - Comparison of Methods for the Wave Equation

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   Lecture 5 - Second-order Wave Equation (including leapfrog)

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   Lecture 6 - Wave Profiles, Heat Equation / point source

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   Lecture 7 - Finite Differences for the Heat Equation

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   Lecture 8 - Convection-Diffusion / Conservation Laws

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   Lecture 9 - Conservation Laws / Analysis / Shocks

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    Lecture 10 - Shocks and Fans from Point Source

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    Lecture 11 - Level Set Method

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    Lecture 12 - Matrices in Difference Equations (1D, 2D, 3D)

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    Lecture 13 - Elimination with Reordering: Sparse Matrices

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    Lecture 14 - Financial Mathematics / Black-Scholes Equation

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    Lecture 15 - Iterative Methods and Preconditioners

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    Lecture 16 - General Methods for Sparse Systems

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    Lecture 17 - Multigrid Methods

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    Lecture 18 - Krylov Methods / Multigrid Continued

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    Lecture 19 - Conjugate Gradient Method

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    Lecture 20 - Fast Poisson Solver

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    Lecture 21 - Optimization with constraints

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    Lecture 22 - Weighted Least Squares

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    Lecture 23 - Calculus of Variations / Weak Form

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    Lecture 24 - Error Estimates / Projections

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    Lecture 25 - Saddle Points / Inf-sup condition

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    Lecture 26 - Two Squares / Equality Constraint Bu = d

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    Lecture 27 - Regularization by Penalty Term

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    Lecture 28 - Linear Programming and Duality

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    Lecture 29 - Duality Puzzle / Inverse Problem / Integral Equations