MATH 481 XGR - Vector and Tensor Analysis
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. Course Information: 3 or 4 undergraduate hours. 3 or 4 graduate hours. 4 hours of credit requires approval of the instructor and department with completion of additional work of substance. Prerequisite: MATH 241 and one of MATH 415 or MATH 416 or equivalent.
This course is available to undergrads as an online Academic Year term offering. See https://netmath.illinois.edu/college/math-481 XGR Section restricted to Engineering Online graduate degree-seeking students in MSAE, MSCE, MCS, MSIE, and MSME degree students. For more details on this course section, please see http://engineering.illinois.edu/online/courses/. Non-degree students please register for MATH 448/461/481 M16 section.
Academic Program Restrictions:
MENG:Bioeng:Gen Bioeng On-UIUC
Option 1Number of Required Visit(s): 0
Course Level: Graduate
Term(s): Fall , Spring , Summer