Transcription of LECTURE NOTES ON APPLIED MATHEMATICS
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LECTURE NOTES ON APPLIED MATHEMATICS
LECTURE NOTES ONAPPLIED MATHEMATICSM ethods and ModelsJohn K. HunterDepartment of MathematicsUniversity of California, DavisJune 17, 2009 Copyrightc 2009 by John K. HunterContentsLecture 1. Introduction11. Conservation laws12. Constitutive equations23. The KPP equation3 LECTURE 2. Dimensional Analysis, Scaling, and Similarity111. Systems of units112. Scaling123. Nondimensionalization134. Fluid mechanics135. Stokes formula for the drag on a sphere186. Kolmogorov s 1941 theory of turbulence227. Self-similarity258. The porous medium equation279. Continuous symmetries of differential equations33 LECTURE 3. The Calculus of Variations431. Motion of a particle in a conservative force field442. The Euler-Lagrange equation493. Newton s problem of minimal resistance514. Constrained variational principles565. Elastic rods576. Buckling and bifurcation theory617. Laplace s equation698.
Jun 17, 2009 · of a concept of seemingly great generality is in essence the same as a small and concrete special case.1 We begin by describing a rather general framework for the derivation of PDEs that describe the conservation, or balance, of some quantity. 1. Conservation laws We consider a quantity Qthat varies in space, ~x, and time, t, with density u(~x;t),
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