UNIT 1:
Double integration (Cartesian Coordinates)
Double integration (Cartesian Coordinates)
Applications of double integral(Area)
Triple Integration(Cartesian Coordinates)
Double integration (Cartesian Coordinates)
Double integration (Cartesian Coordinates)
Change of order of integration
Change of order of integration
Applications of double integral(Area)
Triple Integration(Cartesian Coordinates)
Triple Integration(Cartesian Coordinates)
Applications: Volume as triple integrals and solids of revolution.
Applications: Volume as triple integrals and solids of revolution.
UNIT 2:
Derivatives: Gradient of a scalar field, Directional Derivative
Problems based on Gauss Divergence theorem
Problems based on Green’s theorem
Solenoidal and Irrotational of a vector
Problems based on Stoke’s theorem
Calculating area using double integration
Derivatives: Gradient of a scalar field, Directional Derivative
Green’s theorem(Statement only)
Problems based on Green’s theorem
Gauss Divergence 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:
Zeros & Singularities of an analytic function
Problems based on Cauchy’s integral formula
UNIT 5:
Conditions -Transforms of standard functions , Properties
Transforms of derivatives and integrals
Unit step function (Heaviside function)& Dirac’s Delta function
Laplace transform of periodic functions
Inverse Laplace transforms
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