Tamás Darvas 
Professor, University of Maryland
Summer 2026: "SMI: Differential forms on manifolds"
Description: This course is an introduction to differential forms on manifolds and their applications. The exterior differential calculus of Elie Cartan is one of the most successful and illuminating techniques for calculations. The fundamental theorems of multivariable calculus are united in a general Stokes theorem which holds for smooth manifolds in any number of dimensions. This course develops this theory and technique to perform calculations in analysis and geometry. A solid background in real analysis, multivariable calculus, and linear algebra. Mastery of both topology and the theory of surfaces is not required (but one is strongly preferred). Local calculations relate to global topological invariants, as exemplified by the Gauss-Bonnet theorem.
Textbook: 0) A. Hatcher, Notes on point-set topology (pdf), 1) M.P. do Carmo, Differential Forms and Applications (pdf).
Assignments: weekly homeworks, one final exam (100%).
Classes: MTuWThF, according to SMI SCHEDULE.
Exercise Sessions: TuF, according to SMI SCHEDULE.
Office hours: Friday 15:50 to 16:50 in my office (room 610).
Exam date: Thursday, August 13, 8:30am-10:00am.
Homeworks: Assigned every week: Homework 1 (with solutions), Poll
Homeworks: Assigned every week: Homework 2