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The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines.
FREE
This course includes
Hours of videos
916 years, 6 months
Units & Quizzes
33
Unlimited Lifetime access
Access on mobile app
Certificate of Completion
The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc
Course Currilcum
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- Incompressible flow in elastic wall pipes Unlimited
- Branch points and branch cuts Unlimited
- Conservation laws in continuum modeling Unlimited
- Simplest car following traffic flow model Unlimited
- Discrete to continuum modeling Unlimited
- Weakly nonlinear oscillators Unlimited
- Hopf bifurcations Unlimited
- Weakly nonlinear breathers Unlimited
- Stability of numerical schemes for partial differential equations Unlimited
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- Mechanics of the course. Unlimited
- Conservation laws and PDE. Unlimited
- Classification of PDE. Unlimited
- First order scalar PDE. Unlimited
- Domains of influence and dependence. Unlimited
- Graphical interpretation of solution by characteristics. Unlimited
- Region of multiple values. Envelope of characteristics. Unlimited
- More on envelopes. Infinite slopes at envelope. Unlimited
- Shocks in the presence of source terms. Example. Unlimited
- The Riemann problem for the kinematic wave equation with convex/concave flux. Unlimited
- Shock structure and detailed physics. Unlimited
- Shallow water and higher order terms. Unlimited
- PDE and propagation of information. Unlimited
- Hyperbolicity and weak singularities Unlimited
- Continue with Hamilton-Jacobi equation Unlimited
- Eikonal. Focusing and caustics Unlimited
- Eikonal. Amplitude and curvature along rays. Unlimited
- First order 1-D systems of equations. Classification. Unlimited
- Examples of first order 1-D hypebolic systems. Unlimited
- Gas dynamics in 1-D. Characteristics, simple waves, Unlimited
- Linear equations. Superposition. Unlimited
- Green’s functions for signaling and source terms Unlimited
- Generalized functions. Unlimited
- Green’s function. Poisson equation. Stokes equation. Unlimited
