DIFFERENTIAL AND DIFFERENCE EQUATIONS
Linear differential equation of first order first degree and its reducible forms, Exact differential equation and equation which can be made exact using Integral Factor, First order higher degree differential equations solvable for x, y, p, Clairaut’s form.
Linear differential equation with constant coefficients, Complimentary function and particular integral, Homogeneous linear differential equations with variable coefficient, Simultaneous differential equations.
Linear differential equation of second order: Linear independence of solutions, Solution by transformation of the equations by changing the dependent and independent variable, Factorization of operators, Method of variation of parameters, Method of undetermined coefficients.
Partial differential equations of the first order, Lagrange’s linear equation, Charpit’s general method of solution, Homogeneous linear partial differential equations with constant coefficients, Equations reducible to equations with constant coefficients.
Difference equation: Definition and order of difference equation, first and higher order homogeneous linear difference equations, Difference equation reducible to homogenous form, Non-homogeneous linear difference equation, Complementary functions, Particular integrals.
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- J. L. Bansal and H.S. Dhami, Differential Equations, JPH, 2012.
- K.K. Gupta and D.C. Agarwal, Linear Difference Equation, Krishna Prakashan, 2004.
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- Walter G. Kelley, Allan C. Peterson, Difference Equation: An Introduction with Applications, Academic Press London, 2001.
- Saber Elaydi, An Introduction to Difference Equation, Springer, 2005.
