Advanced Differential Equations
Paper Code:
MAT123
Credits:
5
Contact Hours:
75.00
Max. Marks:
100.00
Unit I:
I
15.00
Non-linear ordinary differential equations of particular forms. Riccati's equation -General solution and the solution when one, two or three particular solutions are known. Total Differential equations.
Unit II:
II
15.00
Partial differential equation of first order – formulation and classification of partial differential equations, Lagrange’s linear equation, particular forms of non – linear partial differential equations of first order, Charpit’s method.
Unit III:
III
15.00
Linear Partial differential equations with constant coefficients. Homogeneous and non- Homogeneous equation.
Unit IV:
IV
15.00
Second order Partial Differential equations – formulation and classification of Second Order Partial Differential equations, Monge’s methods- Canonical forms, classification of Second order Partial differential equations of the type Rr+Ss+Tt+f(x,y,z,p,q)=0 and second order Partial differential equations in more than two independent variables. Method of separation of variables, Laplace, Wave and diffusion equations..
Unit V:
V
15.00
Linear homogeneous boundary value problems. Eigen values and eigen functions. Strum-Liouville boundary value problems. Orthogonality of eigen functions. Reality of eigen values.
Essential Readings:
- D.A.Murray, Introductory course on Differential Equations, Orient Longman
- I. N. Sneddon, Elements of Partial Differential Equations , TMH
- Zafar Ahsan, Differential Equations & their applications, PHI ,New Delhi.
- Prof. J.L.Bansal &Dhami,Differential Equations,JPH Vol. I&II
References:
- A.R.Forsyth , A Treatise on Differential Equations , Macmillan and Co. Ltd, London
- Frank Ayres, Theory and Problems of Differential Equations, TMH.
Academic Year:
