UNIT 1:
Double integration (Cartesian Coordinates)
Change of order of integration
Triple Integration(Cartesian Coordinates)
Double integration (Cartesian Coordinates)
Change of order of integration
Applications of double integral(Area)
Applications of double integral(Area)
Triple Integration(Cartesian Coordinates)
Applications: Volume as triple integrals and solids of revolution.
UNIT 2:
Derivatives: Gradient of a scalar field, Directional Derivative
Divergence & Curl of a vector field
Solenoidal and Irrotational of a vector
Problems based on Green’s theorem
Problems based on Gauss Divergence theorem
Stoke’s theorem(Statement only)
Problems based on Stoke’s theorem
Green’s theorem(Statement only)
Gauss Divergence theorem(Statement only)
UNIT 3:
Derivatives of f(z) - Analytic function
Construction of Analytic functions
UNIT 4:
Cauchy’s integral theorem
UNIT 5:
Conditions -Transforms of standard functions , Properties
Laplace transform of periodic functions
Inverse Laplace transforms
Applications to solution of linear ordinary differential equations of second order with constant coefficients
Applications to solution of linear ordinary differential equations of second order with constant coefficients
Unit step function (Heaviside function)& Dirac’s Delta function
Transforms of derivatives and integrals