MATH 415 - Advanced Applied Mathematics

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Recommended prior course: MATH 365 This two-part class covers the basics of vector calculus in part I, and an introduction to calculus of variations in part II. Part I will include line integrals, the fundamental theorem of line integrals, forms of Green's Theorem, surface area and surface integrals, and the theorems of Gauss and Stokes. Part II will cover the concepts of functionals, various representations of the Euler-Lagrange Equation, numerical techniques including weighted residuals, optimizing functional expressions with constraints, and applications to dynamics, structure of materials, geodesics and quantum mechanics.
Prerequisites: MATH 230