UNIT 1:
Derivatives: Gradient and Directional Derivative
Divergence & Curl of a vector field
Solenoidal and Irrotational of a vector
Application in evaluating line, surface and volume integrals.
Stoke’s theorem with problems
Problems based on Green’s theorem
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
Method of variation of parameters
Method of variation of parameters
Homogeneous equation of Euler’s type
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
UNIT 3:
Derivatives of f(z) - Analytic function
Construction of Analytic functions
Mapping by functions w = c+z, w = cz , w = 1/z
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:
Definitions, properties, existence conditions
Transform of elementary function
Transforms of derivatives and integrals
Inverse Laplace transforms
Application to Solution of linear second order ordinary differential equations with constant coefficients
Application to Solution of linear second order ordinary differential equations with constant coefficients
