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SYLLABUS

UNIT-1

Linear Differential Equations of Higher Order Definitions - Complete Solution, Operator D, Rules for Finding Complimentary Function, Inverse Operator, Rules for Finding Particular Integral, Method of Variation of Parameters.

UNIT-2

Equations Reducible to Linear Differential Equations Cauchy’s and Legendre’s Linear Equations, Simultaneous Linear Equations with Constant Coefficients, Applications to L-C-R Circuit Problems and Mass Spring System.

UNIT-3

Partial Differential Equations First Order Partial Differential Equations, Solutions of First Order Linear and Non-Linear PDEs. Solutions to Homogeneous and Non-Homogeneous Higher Order Linear partial Differential Equations.

UNIT-4

Vector Differentiation Scalar and Vector Point Functions, Vector Operator Del, Del Applies to Scalar Point Functions - Gradient, Del Applied to Vector Point Functions - Divergence and Curl, Vector Identities.

UNIT-5

Vector Integration Line Integral - Circulation-Work Done, Surface Integral-Flux, Green’s Theorem in the Plane (without proof), Stoke’s Theorem (without proof), Volume Integral, Divergence Theorem (without proof) and Applications of These Theorems.