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ES_APPM 420-1: Asymptotic and Perturbation Methods in Applied Mathematics


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Description

Most mathematical models do not admit exact solutions. Asymptotic and perturbation methods provide powerful techniques for obtaining approximate solutions, which allow one to draw physical conclusions and guide numerical simulations of the model. This course covers such methods addressing the following topics: asymptotic expansions and series; approximate solution of algebraic and transcendental equations; asymptotic behavior of solutions of ODEs near ordinary and singular points; regular and singular problems for ODEs; matched asymptotic expansions, boundary layers; strained coordinates; multiple scales; Mathieu equation and Floquet theory; linear and nonlinear oscillators; equations with slowly varying coefficients; boundary-value problems by multiple scales; Hopf bifurcation.