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Principles of Applied Mathematics >> Content Detail



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LEC #TOPICS
1Introduction: Dense Granular Flow in a Silo
2-3Linear Waves: PDE for Waves in an Elastic Medium, Characteristics, d'Alembert's Solution
4-13Nonlinear Kinematic Waves: Lighthill-Whitham Theory of Traffic Flow, Density Waves, General Method of Characteristics, Hodograph Method, Expansion Fans, Wave Breaking, Shocks

River Waves, Gas Compression Waves, Shallow Water Waves
Midterm Exam
14-16Dispersive Waves: Fourier Transform, Group Velocity and Caustics

Envelope Equations, KdV Equation, Solitons
17-18Linear Diffusion: Green Function for the Diffusion Equation, Some Fourier Analysis

Similarity Solutions
19-25Nonlinear Diffusion: Burgers Equation and Shock Structure, Cole-Hopf Transformation

Porous Medium Equation, Similarity Solutions

Regular and Singular Perturbations, Boundary Layers, Matched Asymptotic Expansions

Nernst-Planck Equations
Final Exam

 








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