Details of MA5103 (Autumn 2019)

Level: 5 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA5103 Partial Differential Equations Rajib Dutta,
Saugata Bandyopadhyay,
Shirshendu Chowdhury

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.

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


Suggested Texts:

  1. Evans, L.C., Partial Differential Equations, American Mathematical Society.

  2. Folland, G., Introduction to Partial Differential Equations, Princeton University Press.

  3. Gilbarg, D. and Trudinger, N., Elliptic Partial Differential Equations of Second Order, Springer-Verlag.

  4. Han, Q., A Basic Course in Partial Differential Equations, American Mathematical Society.

  5. John, F., Partial Differential Equations, Springer-Verlag.

  6. McOwen, R.C., Partial Differential Equations: Methods and Applications, Pearson Education.

  7. Renardy, M. and Rogers, R., An Introduction to Partial Differential Equations, Springer-Verlag.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse 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