This is a rigorous course in multivariable analysis. Continuation of MAT215/217 (or MAT203/204, with instructor's permission). It covers differentiation and integration in several variables, including both theoretical results (with fairly detailed proofs) as well as explicit calculations, to ensure both an understanding of the theory and the ability to apply it to concrete problems.
The primary reading comes from the Lecture Notes prepared by Professor R. C. Gunning. In addition the following supplementary texts will be on reserve in the math library:
- An alternate treatment of the more challenging ideas: Calculus on Manifolds by M. Spivak (Benjamin, 1965)
- The usual textbook for our intermediate vector calculus course (MAT203) to help you brush up on/master the basic calculations: Vector Calculus by J. Marsden and A. Tromba (Freeman, 1996)
- Similar to Marsden and Tromba: Advanced Calculus by G. Folland (Prentice Hall, 2002)
The treatment in the course follows most closely that in Spivak's book. The treatments in Folland and in Marsden and Tromba follow the more traditional paths, but these books have a number of useful illustrative problems and more detailed discussions of techniques for solving the problems.