UNIT 1:
Double integration (Cartesian Coordinates)
Double integration (Cartesian Coordinates)
Change of order of integration
Change of order of integration
Applications of double integral(Area)
Applications of double integral(Area)
Triple Integration(Cartesian Coordinates)
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
Divergence & Curl of a vector field
Solenoidal and Irrotational of a vector
Green’s theorem(Statement only)
Problems based on Green’s theorem
Gauss Divergence theorem(Statement only)
Problems based on Gauss Divergence theorem
Stoke’s theorem(Statement only)
UNIT 3:
Derivatives of f(z) - Analytic function
Construction of Analytic functions
Conformality of w = c+z, w = cz , w = 1/z
Application to flow problems
UNIT 4:
Cauchy’s integral theorem
Problems based on Cauchy’s integral formula
Problems based on Cauchy’s integral formula
UNIT 5:
Conditions -Transforms of standard functions , Properties
Transforms of derivatives and integrals
Laplace transform of periodic functions
Applications to solution of linear ordinary differential equations of second order with constant coefficients
Inverse Laplace transforms
Simultaneous linear equations with constant coefficients