18.311 Principles of Applied Mathematics, Spring 2006
Author(s)Bazant, Martin Z.
Principles of Applied Mathematics
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Introduction to fundamental concepts in "continuous" applied mathematics. Extensive use of demonstrational software. Discussion of computational and modelling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world. From the course home page: Course Description This course introduces fundamental concepts in "continuous'' applied mathematics, with an emphasis on nonlinear partial differential equations (PDEs). Topics include linear and nonlinear waves: kinematic waves, method of characteristics, expansion fans, wave breaking, shock dynamics, shock structure; linear and nonlinear diffusion: Green functions, Fourier transform, similarity solutions, boundary layers, Nernst-Planck equations. Applications include traffic flow, gas dynamics, and granular flow.
Linear and nonlinear waves, hyperbolic waves, kinematic waves, expansion fans, shock dynamics, shock structure, Linear diffusion, nonlinear diffusion, Green functions, Fourier transform, dimensional analysis, similarity solutions, boundary layers, traffic flow, gas dynamics, tsunamis, heat transfer, ion transport, granular flow
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