Engineering is a branch of science that will require practitioners to learn mathematical methods. Applying Mathematics to complex engineering problems is possible if you know the theory of practical engineering and scientific computing which this course discusses.
Rest assured that you would apply what you learned in this [course_title] to real-life engineering problems. This course will focus on topics about numerical methods, initial-value problems, and network flows.
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
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Course Credit: MIT
|Lecture 1: Difference Methods for Ordinary Differential Equations||00:45:00|
|Lecture 2: Finite Differences, Accuracy, Stability, Convergence||00:56:00|
|Lecture 3: The One-way Wave Equation and CFL / von Neumann Stability||00:56:00|
|Lecture 4: Comparison of Methods for the Wave Equation||00:52:00|
|Lecture 5: Second-order Wave Equation (including leapfrog)||00:55:00|
|Lecture 6: Wave Profiles, Heat Equation / point source||00:52:00|
|Lecture 7: Finite Differences for the Heat Equation||00:55:00|
|Lecture 8: Convection-Diffusion / Conservation Laws||00:54:00|
|Lecture 9: Conservation Laws / Analysis / Shocks||00:44:00|
|Lecture 10: Shocks and Fans from Point Source||00:56:00|
|Lecture 11: Level Set Method||00:54:00|
|Lecture 12: Matrices in Difference Equations (1D, 2D, 3D)||00:54:00|
|Lecture 13: Elimination with Reordering: Sparse Matrices||00:56:00|
|Lecture 14: Financial Mathematics / Black-Scholes Equation||00:50:00|
|Lecture 15: Iterative Methods and Preconditioners||00:52:00|
|Lecture 16: General Methods for Sparse Systems||00:47:00|
|Lecture 17: Multigrid Methods||00:51:00|
|Lecture 18: Krylov Methods / Multigrid Continued||00:50:00|
|Lecture 19: Conjugate Gradient Method||00:52:00|
|Lecture 20: Fast Poisson Solver||00:48:00|
|Lecture 21: Optimization with constraints||00:51:00|
|Lecture 22: Weighted Least Squares||00:52:00|
|Lecture 23: Calculus of Variations / Weak Form||00:52:00|
|Lecture 24: Error Estimates / Projections||00:50:00|
|Lecture 25: Saddle Points / Inf-sup condition||00:51:00|
|Lecture 26: Two Squares / Equality Constraint Bu = d||00:53:00|
|Lecture 27: Regularization by Penalty Term||00:49:00|
|Lecture 28: Linear Programming and Duality||00:57:00|
|Lecture 29: Duality Puzzle / Inverse Problem / Integral Equations||00:51:00|
|Submit Your Assignment||00:00:00|
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