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.

Jun 17, 2009 · 2 Since this equation holds for arbitrary regions , it follows that, for smooth func-tions, (1.2) u t= r ~q+ ˙: Equation (1.2) is the di erential form of conservation of Q. When the source term ˙is nonzero, (1.2) is often called, with more accuracy, a balance law for Q, rather than a conservation law, but we won’t insist on this distinction. 2.

  Notes, Form, Mathematics, Applied, Applied mathematics