Details of MA5102 (Autumn 2025)
Level: 5 | Type: Theory | Credits: 4.0 |
Course Code | Course Name | Instructor(s) |
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MA5102 | Partial Differential Equations | Sayan Bagchi |
Syllabus |
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First-order Equations: Method of characteristics and existence of local solutions.
Characteristic Manifolds and Cauchy Problem: Non-characteristic surfaces, Cauchy-Kowalevski theorem and uniqueness theorem of Holmgren. Laplace Equation: Fundamental solution, harmonic function and its properties, Poissons equation, Dirichlet problem and Greens function, existence of solution of the Dirichlet problem using Perrons method, introduction to variational method. Heat Equation: Fundamental solution and initial-value problem, mean value formula, maximum principle, uniqueness and regularity, nonnegative solutions, Fourier transform methods. Wave Equation: dAlemberts formula, method of spherical means, Hadamards method of descent, Dumahels principle and Cauchy problem, initial-boundary-value problem, Fourier transform methods. |
Prerequisite |
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Ordinary Differential Equations (MA4202) and Fourier Analysis (MA4205) |
References |
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Suggested Texts:
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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 | MP | 1 | Not Allowed |
5 | MP | 3 | Core |
6 | MR | 1 | Not Allowed |
7 | MR | 3 | Not Allowed |
8 | MS | 3 | Not Allowed |
9 | MS | 5 | Not Allowed |
10 | MS | 7 | Not Allowed |
11 | MS | 9 | Core |
12 | RS | 1 | Elective |
13 | RS | 2 | Elective |