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.
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 four cases).
Calculus of variation: Functionals, Variation of a functional and its properties, Variational problems with fixed boundaries, Euler's equation and it’s alternate forms, Extremals, Functional dependent on several unknown functions and their first order derivatives, Functionals dependent on higher order derivatives, Functionals dependent on the function of more than one independent variable.
Variational problem in parametric forms, Isoperimetric problem and conditions, Geodesic problems, Variational problems with moving (or free) boundaries, One sided variations only for a functional dependent in one or two functions.
- Zafar Ahsan, Differential Equations & Their Applications, PHI, New Delhi, 2016.
- J.L.Bansal & H.S Dhami, Differential Equations, Jaipur Publishing House Jaipur, 2014.
- I.N.Sneddon, Elements of Partial Differential Equations, Mc-Graw Hill, 2006.
- M.D.Raisinghania, Advanced differential equation, S. Chand and Co. Ltd., 2012.
- A.R. Forsyth, A Treatise on Differential Equations, Macmillan and Co. Ltd, London, 956.
- Frank Ayres, Schaum’s Theory and Problems of Differential Equations, Mc-Graw Hill,2012.
- D.A. Murray, Introductory Course in Differential Equations, University of Michigan Library, 1902.
- W.E. Boyce and P.C. Diprima, Elementary Differential Equations and Boundary Value Problems, John Wiley, 1986.
- E.A. Coddington, An Introduction to Ordinary Differential Equations, PHI New Delhi, 2003
- G.F. Simmons, Differential Equations with Applications and Historical Notes, McGraw Hill, New York, 1972.
- E.D. Ranville, Elementary Differential Equations, Macmillan Company, New York, 1964.
