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LECTURE NOTES ON APPLIED MATHEMATICS

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LECTURE NOTES ONAPPLIED MATHEMATICSMethods and ModelsJohn K. HunterDepartment of MathematicsUniversity of California, DavisJune 17, 2009Copyrightc 2009 by John K. HunterContentsLecture 1. Introduction11. Conservation laws12. Constitutive equations23. The KPP equation3Lecture 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 equations33Lecture 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.

LECTURE 1 Introduction The source of all great mathematics is the special case, the con-crete example. It is frequent in mathematics that every instance

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