Details of MA5103 (Autumn 2019)
Level: 5  Type: Theory  Credits: 4.0 
Course Code  Course Name  Instructor(s) 

MA5103  Partial Differential Equations  Rajib Dutta, Saugata Bandyopadhyay, Shirshendu Chowdhury 
Syllabus 

Firstorder Equations: Method of characteristics and existence of local solutions.
Characteristic Manifolds and Cauchy Problem: Noncharacteristic surfaces, CauchyKowalevski 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 initialvalue 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, initialboundaryvalue problem, Fourier transform methods. 
Prerequisite 

Ordinary Differential Equations (MA4202) and Fourier Analysis (MA4205) 
References 

Suggested Texts:

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  9  Core 
7  RS  1  Not Allowed 
8  RS  2  Not Allowed 