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 -

  • Understand the importance of Picard’s theorem.
  • Get introduced with homogeneous and non-homogeneous linear ODE.
  • find the solution of differential equations in the form of infinite series by the Frobenius method.
  • Get familiar with Bessel’s and Legendre’s equations.
  • 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

DMAT 511A

 

 

 

 

Ordinary Differential Equations

 (Theory)

 

 

 

 

 

 

 

The students will be able to –

 

CO122: Gain knowledge about Lipschitz condition and Picard’s Theorem, 2nd order homogeneous equations, properties and applications of Wronskian.

CO123: Gain a clear concept of power series solution of a differential equation about an ordinary point and solution about a regular singular point.

CO124: Make a clear concept of Linear homogeneous and non-homogeneous equations of higher order with constant coefficients, Euler’s equation.

CO125: Know the Power series solution of D.E. and also understand the ordinary and singular points of an O.D.E.

CO126: 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: 
2022-2023
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