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Euclidean space R^n (topology, norms, inner products, continuous functions, contractions, homeomorphisms). Spaces and sequences of functions. Differentiation and integration in finite dimensions (the derivative, partial derivatives, inverse function theorem, implicit function theorem, higher order derivatives, Fubini's Theorem, Change of Variables Theorem). Differential forms. Integration of differential forms. Stokes' Theorem. Credit is not allowed for both ²Ñ´¡Ìý426 and ²Ñ´¡Ìý512.

Prerequisite: ²Ñ´¡Ìý425 or ²Ñ´¡Ìý511 and ²Ñ´¡Ìý405

Typically offered in Fall and Spring