Course Schedule and Catalog
Course Catalog - 2024-2025
MATH 451 - DIFFERENTIABLE MANIFOLDS
Long Title: DIFFERENTIABLE MANIFOLDS
Department: Mathematics
Grade Mode: Standard Letter
Language of Instruction: Taught in English
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Undergraduate Professional
Visiting Undergraduate
Undergraduate
Prerequisite(s): (MATH 354 OR MATH 355) AND (MATH 321 OR MATH 331) AND MATH 443
Description: This is a course on differentiable manifolds. Topics include: Differential of a smooth map. Transversality. Implicit function theorem, submersions, and immersions. Tangent and Cotangent bundles. Vector fields, flows. Lie derivatives. Lie groups. Differential forms, Integration on manifolds, Stokes theorem. DeRham theory. Additional topics may include distributions and foliations, including the Frobenius Theorem. Graduate/Undergraduate Equivalency: MATH 551. Recommended Prerequisite(s): MATH 444 or MATH 463 or MATH 370 or MATH 401