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: Volume as triple integrals and solids of revolution.
Triple Integration(Cartesian Coordinates)
Applications of double integral(Area)
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
Green’s theorem(Statement only)
Gauss Divergence theorem(Statement only)
Problems based on Gauss Divergence theorem
Problems based on Stoke’s theorem
Problems based on Green’s theorem
Stoke’s theorem(Statement only)
UNIT 3:
Derivatives of f(z) - Analytic function
Conformality of w = c+z, w = cz , w = 1/z
Application to flow problems
Construction of Analytic functions
UNIT 4:
Problems based on Cauchy’s integral formula
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
Unit step function (Heaviside function)& Dirac’s Delta function
Simultaneous linear equations with constant coefficients
