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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.

Jun 17, 2009 · 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. Constrained variational principles 56 5. Elastic rods 57 6. Buckling and bifurcation theory 61 7. Laplace’s equation 69 8. The Euler-Lagrange equation 73 9. The ...

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