PHYS 475
Methods in Mathematical Fluid Dynamics Spring 2016 Division III; Quantative/Formal Reasoning; Cross-listed as MATH475 / PHYS475
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The mathematical study of fluids is an exciting field with applications in areas such as engineering, physics and biology. The applied nature of the subject has led to important developments in aerodynamics and hydrodynamics. From ocean currents and exploding supernovae to weather prediction and even traffic flow, several partial differential equations (pde) have been proposed as models to study fluid phenomena. This course is designed to both, introduce students to some of the techniques used in mathematical fluid dynamics and lay down a foundation for future research in this and other related areas. Briefly, we start with the method of characteristics, a useful tool in the study of pde. Symmetry and geometrical arguments, special solutions, energy methods, particle trajectories, and techniques from ordinary differential equations (ode) are also discussed. A special focus will be on models from hydrodynamics. These include the KdV and the Camasss Holm equations (and generalizations thereof), and the Euler equations of ideal fluids. Mainly, we will be concerned with models whose solutions depend on time and one spatial variable, although depending on student interest and time, we may also investigate higher-dimensional models.
The Class: Type: lecture
Limit: 40
Expected: 25
Class#: 3934
Requirements/Evaluation: problem sets and final project
Extra Info: may not be taken on a pass/fail basis
Prerequisites: MATH 151, MATH 250, and MATH 350 or 351; some background in pde/ode would be helpful but not required
Enrollment Preference: senior Mathematics majors
Distributions: Division III; Quantative/Formal Reasoning;

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