UNIT 1:
Solenoidal and Irrotational of a vector
Derivatives: Gradient and Directional Derivative.
Problems based on Green’s theorem
Problems based on Gauss Divergence theorem
Stoke’s theorem with problems
Application in evaluating line, surface and volume integrals.
Derivatives: Gradient and Directional Derivative
UNIT 2:
Higher order linear differential equations with constant coefficients
Problems based on higher order linear differential equations with constant coefficients
Problems based on higher order linear differential equations with constant coefficients
Homogeneous equation of Legendre’s type
Solution of system of simultaneous linear first order differential equations with constant coefficients
Solution of system of simultaneous linear first order differential equations with constant coefficients
Method of variation of parameters
Method of variation of parameters
UNIT 3:
Derivatives of f(z) - Analytic function
Construction of Analytic functions
UNIT 4:
Cauchy’s integral theorem
Problems based on Cauchy’s integral formula
Problems based on Cauchy’s integral formula
Zeros & Singularities of an analytic function
UNIT 5:
Laplace transform of periodic functions
Inverse Laplace transforms
Definitions, properties, existence conditions
Transforms of derivatives and integrals
Solution of linear second order ordinary differential equations with constant coefficients
Solution of linear second order ordinary differential equations with constant coefficients