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