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MATH 481 XGR - Vector and Tensor Analysis

Campus: Urbana-Champaign


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.

Special Instructions:

"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. For more details on this course section, see https://grainger.illinois.edu/academics/online/courses Non-degree students please register for MATH 481 M16 section. Restriction(s) Restricted to MS: Civil Engr - Online - UIUC, MCS:Computer Sci Online -UIUC, MS:Industrial Engr Online-UIUC, MS:Mechanical Engineerng -UIUC, MS:Env Engr CivilEngr ONL-UIUC, MS: Aerospace Engr-Online-UIUC, MENG:Engr:Energy Sys Onl-UIUC, NDEG:Grad Nondegree-CE-UIUC, MENG:Mech Engineering Onl-UIUC, MENG:Engr:AeroSys Online- UIUC, or MENG:Engr:Plasma Online-UIUC."

Academic Program Restrictions:

MENG:Engr:AeroSys Online- UIUC

Option 1

Number of Required Visit(s): 0

Course Level: Graduate

Credit: 3

Term(s): Fall , Spring , Summer


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