Details of MA5116 (Autumn 2020)
| Level: 5 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA5116 | Introduction to PDE and Distribution Theory | Rajib Dutta |
| Syllabus |
|---|
| Frist-Order PDEs: Linear, semilinear, quasilinear equations; The method of characteristics; The existence and uniqueness theorem.
Distribution Theory: Test functions, distributions, basic properties of distributions, support and singular support of distributions, convolution of distributions, Fourier transform, Schwartz spaces, tempered distributions, fundamental solution. Sobolev Spaces: Basic properties of Sobolev spaces, approximation by smooth function, extension theorem, embedding theorem, compactness theorem. |
| Prerequisite |
|---|
| Functional Analysis (MA4102) and Ordinary Differential Equations (MA4202)
|
| References |
|---|
| Suggested texts:
1. Pinchover, Y. and Rubinstein, J. An Introduction to Partial Differential Equations. 2. Kesavan, S. Topics in Functional Analysis and applications. 3. Evans, L. Partial Differential Equations. 4. Brezis, H. Functional Analysis, Sobolev Spaces and Partial Differential Equations. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | IP | 5 | Not Allowed |
| 4 | MR | 1 | Not Allowed |
| 5 | MR | 3 | Not Allowed |
| 6 | MS | 5 | Not Allowed |
| 7 | MS | 7 | Not Allowed |
| 8 | MS | 9 | Elective |
| 9 | RS | 1 | Elective |
| 10 | RS | 2 | Not Allowed |