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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.

Jun 17, 2009 · Lecture 1. Introduction 1 1. Conservation laws 1 2. Constitutive equations 2 3. The KPP equation 3 Lecture 2. Dimensional Analysis, Scaling, and Similarity 11 1. Systems of units 11 2. Scaling 12 3. Nondimensionalization 13 4. Fluid mechanics 13 5. Stokes formula for the drag on a sphere 18 6. Kolmogorov’s 1941 theory of turbulence 22 7. Self ...

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