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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.
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English
English [CC]
FREE
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Description
The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc
Course content
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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
Instructor
Massachusetts Institute of Technology
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1916
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