Advanced Differential Equations
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.
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.
Linear Partial differential equations with constant coefficients. Homogeneous and non- Homogeneous equation.
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..
Linear homogeneous boundary value problems. Eigen values and eigen functions. Strum-Liouville boundary value problems. Orthogonality of eigen functions. Reality of eigen values, Series solution:- All three cases.
- Zafar Ahsan, Differential Equations & their applications, PHI ,New Delhi.
- Prof. J.L.Bansal &Dhami,Differential Equations,JPH Vol. I&II
- I. N. Sneddon, Elements of Partial Differential Equations , TMH
- A.R.Forsyth , A Treatise on Differential Equations , Macmillan and Co. Ltd, London
- Frank Ayres, Theory and Problems of Differential Equations, TMH.
- D.A.Murray, Introductory course on Differential Equations, Orient Longman.
