Partial Differential Equations

Paper Code: 
DMAT 611A
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Classify the fundamental principles of partial differential equations(PDEs) to solve hyperbolic, parabolic and elliptic equations.
  2. Apply a range of techniques to find solutions of standard Partial Differential Equations (PDE).

Course Outcomes (Cos):

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

DMAT611A

 

 

 

 

 

 

 

Partial Differential Equations

 (Theory)

 

 

 

 

 

 

The students will be able to –

 

CO116: Solve Linear Homogeneous Partial differential equations with constant coefficients using appropriate methods.

CO117: Apply analytical methods to solve Non-Linear Homogeneous Partial differential equations with constant coefficients.

CO118: Describe the concept of Elliptic differential equations and find their solutions.

CO119: Understand the concept of Parabolic differential equations and find solutions using appropriate methods.

CO120: Equip with the concepts of Hyperbolic differential equations and to solve PDEs with different analytical methods.

 

Approach in teaching:

 

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Giving tasks

 

 

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
I
18.00

Partial differential equations of second order: Linear Homogeneous partial differential equations with constant coefficients and their solutions.

Unit II: 
II
18.00

Non-Homogeneous linear partial differential equations with constant coefficients, Reducible to linear partial differential equations.

Unit III: 
III
18.00

Elliptic Differential equations: Solution of Boundary Value Problems by the method of separation of Variables, Laplace equation in Cartesian and polar coordinates, Solution of Laplace equation of two dimension.

Unit IV: 
IV
18.00

Parabolic Differential equations: Heat equation, solution of one and two dimensional Heat equation in Cartesian Coordinates, Uniqueness of the solution and Maximum-Minimum principle.

Unit V: 
V
18.00

Hyperbolic Differential equations: Derivation of one and two dimension Wave equation and their solution, D’Alembert’s solution of Wave equation, Uniqueness of the solution for the Wave equation. 

Essential Readings: 
  • S.K. Pundir and Rimple Pundir,” Advanced partial differential Equations(with Boundary value problems)”, Pragati Prakashan.
  • Raisinghania, M. D. Advanced Differential Equations. S. Chand & Company Ltd. New Delhi, 2001.
  • Raisinghania, M. D. Ordinary and Partial Differential Equations. S. Chand & Company Ltd. New Delhi.
References: 
  • Sneddon, I.N. (1957) Elements of Partial Differential Equations, McGraw Hill.
  • Fritz John (1982) Partial Differential Equations, Springer-Verlag, New York Inc.
  • S.L. Ross, Differential equations, 3rd Ed., John Wiley and Sons, India, 2004.
 
Academic Year: 
2023-2024
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