Ordinary Differential Equations

Paper Code: 
24DMAT515(A)
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: 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

24DMAT

515(A)

 

 

 

 

Ordinary Differential Equations

 (Theory)

 

 

 

 

 

 

 

CO111: Explore about the properties and uses of Wronskian, the Lipschitz condition, Picard's Theorem and second-order homogeneous equations.

CO112: Develop an in-depth knowledge of the power series solution for both the regular singular point solution and the differential equation for an ordinary point.

CO113: Explain linear, higher-order, homogeneous and non-homogeneous equations with constant coefficients, including Euler's equation.

CO114: Analyze the power series solution of D.E. and also understand the ordinary and singular points of an O.D.E.

CO115: Solve higher order equations, qualitative analysis of special functions.

CO116: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Assigned tasks

 

 

 

 

Quiz, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
Existence of solutions to Differential Equations
18.00

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

 

Unit II: 
Singular Solutions, Geometrical meaning of differential equations and orthogonal trajectories, Chebyshev polynomial
18.00

Orthogonal properties, recurrence relation, generating functions.

 

Unit III: 
Linear dependence and independence via Wronksian
18.00

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

 

Unit IV: 
Series solutions
18.00

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

 

Unit V: 
Special Functions
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.

e- RESOURCES

 

JOURNALS

 

 

 

 

Academic Year: 
2024-2025
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