18.311 Principles of Applied Mathematics, Spring 2006
Name
18-311Spring-2006/OcwWeb/Mathematics/18-311Spring-2006/CourseHome/index.htm
Size
14.19 KB
Format
HTML
Checksum (MD5)
f8a067a5a8a8b46d213f94a7ba35b7db
Author(s)
Bazant, Martin Z.
Alternative Title
Principles of Applied Mathematics
Date Issued
June 2006
Abstract
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.
Subjects
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
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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