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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. The Euler-Lagrange equation493. Newton s problem of minimal resistance514. Constrained variational principles565. Elastic rods576. Buckling and bifurcation theory617. Laplace s equation698. The Euler-Lagrange equation739. The wave equation7610.

Jun 17, 2009 · 13. Hamiltonian PDEs 86 14. Path integrals 88 Lecture 4. Sturm-Liouville Eigenvalue Problems 95 1. Vibrating strings 96 2. The one-dimensional wave equation 99 3. Quantum mechanics 103 4. The one-dimensional Schr odinger equation 106 5. The Airy equation 116 6. Dispersive wave propagation 118 7. Derivation of the KdV equation for ion-acoustic ...

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