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This course covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, and granular flows. The class also covers continuum limit, conservation laws, quasi-equilibrium, kinematic waves, characteristics, simple waves, shocks, diffusion, finite differences, consistency, stability, discrete and fast Fourier transforms, spectral methods transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity.


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

Conservation Laws in Continuum Modeling (PDF) 00:25:00
Stability of Numerical Schemes for PDEs (PDF) 00:25:00
Simplest Car Following Traffic Flow Model (PDF) 00:30:00
Discrete to Continuum Modeling (PDF) 00:25:00
Separation of Variables (PDF) 00:20:00
Various Lecture Notes (PDF) 00:30:00
Submit Your Assignment 00:00:00
Certification 00:00:00

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