A theoretical second course in calculus for students with a serious interest in mathematics. Topology of R^n; compactness, functions and continuity, extreme value theorem. Derivatives; inverse and implicit function theorems, maxima and minima, Lagrange multipliers. Integration; Fubini's theorem, partitions of unity, change of variables. Differential forms. Manifolds in R^n; integration on manifolds; Stokes' theorem for differential forms and classical versions. Note: MAT257Y5 will be accepted anywhere where MAT232H5 or MAT236H5 are accepted.
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