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Introduction to theory of functions of a complex variable. Evaluation of integrals by residues and other methods. Vector-derivative operations in curvilinear coordinates. Second-order linear differential equations: series and second solutions. Special properties of orthogonal functions: generating functions, recursion relations. Integral transforms. Prerequisites: PHYS 070 PO, or PHYS 041 PO and PHYS 042 PO; and MATH 102 PO.