Course Content    The real number system and finite dimensional Euclidean space: axiomatic introduction of the real numbers, the Euclidean space R^{N}, functions, topology in R^{N}.
 Limits and continuity: limits of sequences, limits of functions, global properties of continuous functions, uniform continuity.
 Differentiation in R^{N}: differentiation of real valued functions of a real variable, partial derivatives, vector fields, total differentiability, Taylor's Theorem, classification of stationary points.
 Integration in R^{N}: content in R^{N}, the Riemann integral in R^{N}, calculation of integrals, Fubini's Theorem, integration in polar, spherical, and cylindrical coordinates.

Textbooks   None required, but the following are recommended.
 Robert G. Bartle, The Elements of Real Analysis, Second Edition. JosseyBass, 1976.
 Patrick M. Fitzpatrick, Advanced Calculus. PWS Publishing Company, 1996.
 James S. Muldowney, Advanced Calculus Lecture Notes for Mathematics 217317, I, Third Edition.
 William R. Wade, An Introduction to Analysis, Second Edition. Prentice Hall, 2000.
I will follow my TeXed lecture notes, which I plan to slightly revise as the term progresses. 