Overview
Introductory course in modern differential geometry focusing on examples, broadly aimed at students in mathematics, the sciences, and engineering. Emphasis on rigorously presented concepts, tools and ideas rather than on proofs. The topics covered include differentiable manifolds, tangent spaces and orientability; vector and tensor fields; differential forms; integration on manifolds and Generalized Stokes' Theorem; Riemannian metrics, Riemannian connections and geodesics. Applications to configuration and phase spaces, Maxwell equations and relativity theory will be discussed.
Note: This XGR section is restricted to students in UIUC Online Graduate Engineering Degree programs. For more details on this course section, see Explore Engineering Online Courses.
Syllabus
Prerequisites:
MATH 241 and one of Math 415 or Math 416 or equivalent.
Credit Hours: 3
Testing
Exams:
This course has two 90-minute midterm tests and a 3-hour final exam.
Exam Information:
Detailed information about how to access exams will be available within the course site.