MSM1103 - Theory of Ordinary Differential Equations

HNGU M.SC. MATHEMATICS SEMESTER - I

 MSM1103 – THEORY OF ORDINARY DIFFERENTIAL EQUATIONS

Unit 1: 

• Simultaneous ordinary differential equations of first order and first degree, 
• Pfaffian method, 
• Total differential equations, 
• Partial differential equations of the first order.

Unit 2: 

• Cauchy’s Problem (Only Statement), 
• Geometrical interpretation, 
• Linear equations,
• Nonlinear equations, 
• Charpit’s method, 
• Jacobi’s method.

Unit 3: 

• Power series solution of linear differential equations - ordinary and singular points of differential equations,
• Classification into regular and irregular singular points,
• Series solution about an ordinary point and a regular singular point - Frobenius method,
• Chebyshev and Gauss Hypergeometric equations and their general solutions.

Unit 4: 

• Generating function, Recurrence relations,
• Rodrigue’s formula Orthogonality properties.
• Behaviour of solution at irregular singular points and the point at infinity.

Download Reference Books:

1. M D Raisinghania, Ordinary and Partial Differential Equations, S Chand & Co.

2. G..F. Simmons: Differential Equations, TMH Edition, New Delhi, 1974

3. E.D. Rainville and P.E. Bedient: Elementary Differential Equations, McGraw Hill, NewYork, 1969.

4. E.A. Coddington and N. Levinson: Theory of Ordinary Differential Equations, McGraw Hill, 1955.

5. A.C. King, J. Billingham& S.R. Otto: Differential equations, Cambridge University Press, 2006.

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