MATH 481 M16 - 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 section is only available in a 16-week self-paced online format as part of the academic year term (not summer term). Registration for the self-paced class is done through https://netmath.illinois.edu/register/college (not self-service). This course features video lectures and online lecture notes through Moodle. No additional textbook has to be purchased. Please contact firstname.lastname@example.org with any questions.
Option 1Number of Required Visit(s): 0
Course Level: Graduate
Term(s): Continuous/Open , Summer