Contents:

Differentiable Mappings, Taylor's Formula, Local Invertibility, Implicit Function Theorem, Morse's Lemma, Differentiable Manifolds, Lagrange Multipliers, Integration Theory, Fubini's Theorem, Change of Variables Formula, Elements of Fourier Analysis.

Particulars: Primary emphasis will be placed on conceptual developments and proofs.

Prerequisite: Math 411 (Real Analysis I).

Textbook:

J. E. Marsden and M. J. Hoffmann, **Elementary Classical Analysis
(Second Edition)**,
W. H. Freeman, San Francisco, 1993.

Last updated December 7, 2017.