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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

Course Curriculum

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
Certification 00:00:00

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