MATH 444 — Calculus on Manifolds-Prerequisite MATH 441
Mathematics · University of Ghana
This course aims to provide an introduction to Differentiable Manifolds and the tools for performing calculus on these objects; tangent vectors and differential forms. We will see how concepts like the derivative in Rn is extended to a smooth n-dimensional manifold. Topics include: manifolds and submanifolds, differentiability of maps between manifolds, the tangent space, the tangent bundle and the tangent functor. Vector bundles. The exterior algebra, the notion of a differentiable form on a manifold, singular n-chains and integration of a form over a chain. Partition of unity. Application to Stokes' theorem.
- Credits
- 3
- Level
- Level 400
- Semester
- Semester Two
Other courses on this programme
- MATH 440 — Abstract Algebra II-Prerequisite MATH 354
- MATH 441 — Advanced Calculus-Prerequisite MATH 351 or MATH 353
- MATH 442 — Integration Theory and Measure –Prerequisite MATH 356
- MATH 443 — Differential Geometry-Prerequisite MATH 355
- MATH 445 — Introductory Functional Analysis-Prerequisite MATH 356
- MATH 446 — Module Theory-Prerequisite MATH 440
- MATH 447 — Complex Analysis-Prerequisite MATH 223
- MATH 448 — Special Relativity- Prerequisite MATH 362
- MATH 449 — Electromagnetic Theory II-Prerequisite MATH 366
- MATH 450 — Differential Equations II-Prerequisite MATH 350
- MATH 451 — Introduction to Algebraic Field Theory-Prerequisite MATH 354
- MATH 452 — Introduction to Lie Groups and Lie Algebras- Prerequisite MATH 354
Practising MATH 444 with Questora
Upload your own slides, notes and past papers for MATH 444 and Questora builds mock exams, practice questions and a revision plan from them.
Start freeCourse details from University of Ghana Volume 3 Handbook for the Bachelor's Degree: Course Descriptions for Programmes in the Sciences (2017).