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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.

Jun 17, 2009 · 6. Kolmogorov’s 1941 theory of turbulence 22 7. Self-similarity 25 8. The porous medium equation 27 9. Continuous symmetries of di erential equations 33 Lecture 3. The Calculus of Variations 43 1. Motion of a particle in a conservative force eld 44 2. The Euler-Lagrange equation 49 3. Newton’s problem of minimal resistance 51 4.

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