Ordinary Differential Equations

Paper Code: 
DMAT 511A
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Understand the importance of Picard’s theorem.
  2. Get introduced with homogeneous and non-homogeneous linear ODE.
  3. find the solution of differential equations in the form of infinite series by the Frobenius method.
  4. Get familiar with Bessel’s and Legendre’s equations.
  5. prove the linear dependence and independence of solutions by Wronskian.

Course Outcomes (COs):

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

DMAT511A

 

 

 

 

 

 

 

 

Ordinary Differential Equations

 (Theory)

 

 

 

 

 

 

 

The students will be able to –

 

CO106: Gain knowledge about Lipschitz condition and Picard’s Theorem, 2nd order homogeneous equations, properties and applications of Wronskian.

CO107: Gain a clear concept of power series solution of a differential equation about an ordinary point and solution about a regular singular point.

CO108: Make a clear concept of Linear homogeneous and non-homogeneous equations of higher order with constant coefficients, Euler’s equation.

CO109: Know the Power series solution of D.E. and also understand the ordinary and singular points of an O.D.E.

CO110: Solve higher order equations, qualitative analysis of special functions.

 

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

First order differential equation: Picard iterative method, Problems of existence and uniqueness: lipschitz condition, Picard’s theorem.

Unit II: 
II
18.00

Singular Solutions , Geometrical meaning of differential equations  and  orthogonal trajectories, Chebyshev polynomial : orthogonal properties, recurrence relation, generating functions.

Unit III: 
III
18.00

Wronksian linear dependence and independence set of function and Existence and uniqueness theorem, related theorem on Wronksian , Abel's  formula .

Unit IV: 
IV
18.00

Series solutions:   Ordinary and singular point , Frobenius method,  series solution near an ordinary point and regular singular points all four cases .

Unit V: 
V
18.00

Solution of hypergeometric, Bessel ‘s and Legendre differential equations for all possible singular points.

Essential Readings: 
  • M.D Raisinghania, Ordinary and Partial Differential  Equations , S.Chand & Company PVT.LTD., 2014.
  • M.D Raisinghania, Advanced  Differential Equations, S.Chand & Company PVT.LTD., 2014
  • S. Balachandra Rao & H.R. Anuradha, Differential Equations with Applications and Programmes, University Press, Hyderabad, 1996.
References: 
  • D.A. Murray, Introductory Course in Differential Equations, Orient Longman , 1967.
  • E. A. Codington, An Introduction to Ordinary Differential Equations, Prentice Hall of India, 1961.
  • B. Rai, D.P. Choudhary & H.I. Freedman, Ordinary Differential Equations, Narosa Publications, New Delhi, 2002.
Academic Year: 
2023-2024
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