Unit I : PARTIAL DIFFERENTIATION
Functions of two variables, Definition of partial derivatives, Chain rule, Euler's Theorem, Implicit function and Differentials. Applications (Approximation, Maxima and Minima).
Unit II : Differential Equations :
Formation of differential equations, Separation of variables, Equation reducible to separation of variables, Homigeneous differential equations. Equations reducible to Homogeneous. Exact differential equations, Linear differential eqations, Bermoulli's differential equations & engineering applications.
Unit III : Linear differential equation of higher order with constant coeffecients. Engineering Applicaions.
Unit IV : Matrices : Rank of matrix, consistency and solution of a system of linear equations. Eigen values of Eigen vectors of matrix Cayley - Hamitton Theorem.
Unit V : Laplace Transform : Definition and formulae, Linearity, First shifting property, Inverse Laplace Transforms of standars functions.
Unit VI : Inverse Laplace Transform of rational functions. Laplace Transforms of derivatives of first and second order. Use of Laplace transforms in solvign Linear differential equations with constant co-efficients.
Books --
1. G.V. Kumbhojkar, Engineering Mathematics, Phadke Prakashan Kolhapur 1995
(II year Diploma).
2. H.K. Das, Advance Engineering Mathematics
>3.Electrical Circuit II
>4.Thermal &Waterpower Engineering
>5.Basic Electronics
