To understand the subject as tool applicable in other branches of Sciences, Engineering and Technology.
To improve analytical skill.
Unit I:
I
10.00
Degree and order of a differential equation .Equations of first order and first degree – Variable separable method , Homogeneous and equations reducible to homogeneous form , Linear and equations reducible to linear form.
Unit II:
II
10.00
Exact differential equations and equation which can be made exact. First order higher degree equations – solvable for x, y, p. Clairaut’s form.
Unit III:
III
15.00
Linear differential equation with constant coefficients, complimentary function and particular integral. Homogeneous linear differential equations with variable coefficient. Simultaneous differential equations . Exact linear differential equations of nth order.
Unit IV:
IV
15.00
Linear differential equations 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.
Unit V:
V
10.00
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.
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.
Bansal and Dhami, Differential Equations, vol. I, JPH, Jaipur
References:
A.R.Forsyth , A Treatise on Differential Equations , Macmillan and Co. Ltd, London
Frank Ayres, Theory and Problems of Differential Equations, TMH.
