ME010302-Partial Differential Equations

Course Code: ME010302                                         Coordinator: Nisha V M

Course Credit: 4

Semester: III

Course Type: Core

Department: Mathematics

COURSE OBJECTIVES:

1. Introduce the difference between Ordinary differential equation and partial differential equations
2. Introduce students to the origin and formation of partial differential equations.
3. Introduce students to how to solve linear and non linear Partial Differential equations using different methods.

LEARNING OUTCOMES:

On successful completion of this course students will be able to:

1. solve linear partial differential equations of both first and second order
2. apply specific methodologies, techniques and resources to conduct research and produce innovative results in the area of specialisation.
3. identify real phenomena as models of partial derivative equations.
4. extract information from partial derivative models in order to interpret reality.
5. Apply partial derivative equation techniques to predict the behaviour of certain phenomena.
6. Analyse, synthesise, organise and plan projects in the field of study

SYLLABUS:

Module 1: (20 hours)

Methods of solutions of dx/P = dy/Q =  dz/R.  Orthogonal trajectories  of a  system of curves on a surface. Pfaffian differential forms and equations. Solution of Pfaffian differential equations in three variables, Partial differential equations. Origins of first order partial differential equation.

Module 2:      (25 hours)

Linear equations of first order.  Integral  surfaces  passing  through  a  given curve. Surfaces orthogonal to a given system of surfaces. Nonlinear partial differential equation of the first order . Compatible systems of first order equations . Charpits Method. Special types of first order equations. Solutions satisfying given conditions.

Module 3:    (20 hours)

Jacobi’ s method The origin of second order  equations.  Linear  partial differential equations with constant coefficients. Equations with variable coefficients.

Module 4.:  (25 hours)

Separation of variables. Non linear equations of the second order . Elementary solutions of Laplace equation. Families of equipotential surfaces. The two dimensional Laplace Equation Relation of the Logarithmic potential to the Theory of Functions.

 Text Book:

Ian Sneddon , Elements of Partial Differential Equations, Mc Graw Hill Book Company

 References:

1. Phoolan Prasad and Renuka Ravindran, Partial Differential Equations, New Age International
2. K Sankara Rao, Introduction to Partial Differential Equations, Prentice Hall of India
3. E T Copson, Partial Differential Equations, S Chand and Co

TEACHING SCHEDULE:

EVALUATION STRATEGY:

The internal evaluation is based on the participant’s attendance, class participation, assignments, seminars and internal assessment and continuous evaluation tests