Ordinary and Partial Differential Equations and Applications

Hello friends. I am Dr. P.N. Agarwal, professor in the Department of Mathematics,
IIT Roorkee and my left side we have Dr. D.N. Pandey, associate professor in the same department. Hello. We extend a very warm welcome to you on our
course ordinary and partial differential equations and applications under the MOOCs programme
of the MHRD Government of India. The objective of the present course is to
familiarize the UG and PG students of engineering and sciences with various mathematical techniques
that are widely used for solving and getting an analytical solution to ordinary and partial
differential equations of first and second order. In the ODE part broadly we will discuss the
existence and uniqueness of solutions of an ODE, homogenous and non-homogenous linear
systems of differential equations, power series and Frobenius series solutions of second order
homogenous differential equations, boundary value problems for second order ODE, Eigen
value problems, problems, Green functions method, autonomous systems, phase plane, critical
points and stability for linear and nonlinear systems. In the PDE part, we discuss the classification
of first order PDE, existence and uniqueness of solutions, nonlinear PDE of first order,
Cauchy method of characteristic, Charpit method, PDE with variable coefficient, canonical forms,
characteristic curves, Laplace equation, Poisson equation, wave equation, homogenous and non-homogenous
heat equation and Duhamel’s principle. We believe that the present course will be
immensely useful for the UG and PG students of engineering and sciences as it has tremendous
applications and diverse fields of engineering and sciences such as control theory, numerical
analysis and dynamical systems. We look forward to interacting with you during
this course. Thank you very much. Thank you.

3 thoughts on “Ordinary and Partial Differential Equations and Applications

Leave a Reply

Your email address will not be published. Required fields are marked *