Details of MA4203 (Spring 2019)
| Level: 4 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA4203 | Differential Geometry | Swarnendu Datta |
| Syllabus |
|---|
| Basic Theory: Topological manifolds, examples, differentiable manifolds and maps, immersed and imbedded manifolds, submanifolds, partitions of unity, compact manifolds as closed submanifolds of R^n;
Tangent Space and Vector Fields: Definition of tangent vector as equivalence class of curves and derivations, tangent spaces and their mappings, tangent bundle, vector fields, integral curves, Lie brackets; Differential Forms and Integration: Wedge product, Exterior differentiation: definition, axiomatic treatment and coordinate invariance, closed and exact forms, review of classical line and surface integrals, orientation, Stokes theorem; deRham Cohomology: Definition, elementary computation for compact orientable surfaces, computation of top cohomology. |
| Prerequisite |
|---|
| MA3101,MA3201 |
| References |
|---|
| Suggested Texts:
1. Guillemin, V. and Pollack, A., Differential Topology, AMS Chelsea. 2. Kumaresan, S., A Course in Differential Geometry and Lie Groups, Hindustan Book Agency. 3. Lee, J.M., Introduction to Smooth Manifolds, Springer-Verlag. 4. Spivak, M., A comprehensive Introduction to Differential Geometry, Vol. I, 3rd Edition, Publish or Perish. 5. Tu, L.W., An Introduction to Manifolds, Universitext, Springer-Verlag. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | IP | 6 | Not Allowed |
| 4 | MR | 2 | Not Allowed |
| 5 | MR | 4 | Not Allowed |
| 6 | MS | 8 | Core |
| 7 | RS | 1 | Not Allowed |
| 8 | RS | 2 | Elective |