Course Content

Our Focus in the second semester will be integration on manifolds. We begin with a study of integration in euclidean n-space, i.e., multiple integration. We will establish the basic properties of integration. We will discuss Fubini's theorem and the use of iterated integrals to calculate multiple integrals. We will then turn to manifolds and define differential forms on a manifold. This leads us to define and study integrals of forms on a manifold. This includes the more familiar line and surface integrals Finally we will prove Stokes' theorem and its special cases in 2 and 3 variables, tying together our work on differentiation and integration.

Basic Course Information

Math 3593H is a 5 credit course. It is the second semester of a yearlong course in multivaiable (vector) calculus and linear algebra.
Lecture: MWF 10:10-11AM, 209 Vincent Hall.
Instructor: Professor S.Sperber.
Email: sperber@math.umn.edu
Office: 457 Vincent Hall
Phone: 612-625-4374
Office Hours: Tentatively Monday 1-2, and Wednesday 12:30-1:30
Textbook: Vector Calculus, Linear Algebra and Differential Forms (A Unified Approach), John and Barbara Burke Hubbard, 4th edition (either printing), 2009, Matrix Editions, ISBN 978-0-9715766-5-0

Recitation: Tues, Thurs, 10:10-11AM, Vincent Hall 206.
Instructor: Ryan Goh

Organization of Course and Grading Policy

There will be two mid-semester in-class exams of 50 minute duration. Exam dates: First midsemester exam is Tuesday, February 18. The second midsemester exam will be on Tuesday, April 1.

There is also a (cumulative) final examination which will be given 1:30 - 4:30pm on Monday, May 12 .

Homework will be collected weekly, every Tuesday in recitation and some, if not all, of your work on problems will be graded.

The final grade will be determined according to the following guide:

mid-semester exams 40%

final 40%

homework and class participation 20%

Course Information

Spring break is March 17 through March 21.