UNIT 1:
Double integration (Cartesian Coordinates)
Double integration (Cartesian Coordinates)
Change of order of integration
Applications: Volume as triple integrals and solids of revolution.
Triple Integration(Cartesian Coordinates)
Triple Integration(Cartesian Coordinates)
Applications: Volume as triple integrals and solids of revolution.
Change of order of integration
Applications of double integral(Area)
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
Problems based on Stoke’s theorem
Green’s theorem(Statement only)
Gauss Divergence theorem(Statement only)
Stoke’s theorem(Statement only)
UNIT 3:
Derivatives of f(z) - Analytic function
Construction of Analytic functions
Application to flow problems
Conformality of 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:
Conditions -Transforms of standard functions , Properties
Transforms of derivatives and integrals
Laplace transform of periodic functions
Inverse Laplace transforms
Applications to solution of linear ordinary differential equations of second order with constant coefficients
Simultaneous linear equations with constant coefficients
Unit step function (Heaviside function)& Dirac’s Delta function