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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.

Jun 17, 2009 · such as the compressible Euler equations for the ow of an inviscid compressible uid [47]. Example 1.2. Suppose that the ux is a linear function of the density gradient, (1.3) ~q= Aru; where A is a second-order tensor, that is a linear map between vectors. It is represented by an n nmatrix with respect to a choice of nbasis vectors. Then,

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