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Last updated:
September 21, 2023
Duration:
Unlimited Duration
FREE
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
Description
18.086 Mathematical Methods for Engineers II (Spring 2006, MIT OCW). This consists of 29 video lectures given by Professor Gilbert Strang, focusing on initial value problems and solutions of large linear systems.
This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization. (from ocw.mit.edu)
Course Curriculum
- Lecture 01 – Difference Methods for Ordinary Differential Equations Unlimited
- Lecture 02 – Finite Differences, Accuracy, Stability, Convergence Unlimited
- Lecture 03 – The One-way Wave Equation and CFL/ von Neumann Stability Unlimited
- Lecture 04 – Comparison of Methods for the Wave Equation Unlimited
- Lecture 05 – Second-order Wave Equation (including leapfrog) Unlimited
- Lecture 06 – Wave Profiles, Heat Equation/ Point Source Unlimited
- Lecture 07 – Finite Differences for the Heat Equation Unlimited
- Lecture 08 – Convection-Diffusion/ Conservation Laws Unlimited
- Lecture 09 – Conservation Laws/ Analysis/ Shocks Unlimited
- Lecture 10 – Shocks and Fans from Point Source Unlimited
- Lecture 11 – Level Set Method Unlimited
- Lecture 12 – Matrices in Difference Equations (1D, 2D, 3D) Unlimited
- Lecture 13 – Elimination with Reordering: Sparse Matrices Unlimited
- Lecture 14 – Financial Mathematics/ Black-Scholes Equation Unlimited
- Lecture 15 – Iterative Methods and Preconditioners Unlimited
- Lecture 16 – General Methods for Sparse Systems Unlimited
- Lecture 17 – Multigrid Methods Unlimited
- Lecture 18 – Krylov Methods/ Multigrid Continued Unlimited
- Lecture 19 – Conjugate Gradient Method Unlimited
- Lecture 20 – Fast Poisson Solver Unlimited
- Lecture 21 – Optimization with Constraints Unlimited
- Lecture 22 – Weighted Least Squares Unlimited
- Lecture 23 – Calculus of Variations/ Weak Form Unlimited
- Lecture 24 – Error Estimates/ Projections Unlimited
- Lecture 25 – Saddle Points/ Inf-sup Condition Unlimited
- Lecture 26 – Two Squares/ Equality Constraint Bu = d Unlimited
- Lecture 27 – Regularization by Penalty Term Unlimited
- Lecture 28 – Linear Programming and Duality Unlimited
- Lecture 29 – Duality Puzzle/ Inverse Problem/ Integral Equations Unlimited
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