UNIT 1:
Double integration (Cartesian co-ordinates)
Double integration (Cartesian co-ordinates)
Change of order of integration
Change of order of integration
Applications of double integral (Area)
Triple Integration (Cartesian co-ordinates)
Applications: Volume as triple integrals and solids of revolution.
Applications: Volume as triple integrals and solids of revolution.
Triple Integration (Cartesian co-ordinates)
UNIT 2:
Derivatives: Gradient of a scalar field. Directional derivative
Divergence of a vector field & Curl of a vector field
Solenoidal and Irrotational of a vector
Problems based on Gauss divergence Theorem
Problems based on Stokes formula
UNIT 3:
Derivatives of f(z) – Analytic function
Construction of Analytic function
Conformality of w= z + c, cz , 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
Zeros of an analytic function and singularities
UNIT 5:
Conditions – Transforms of elementary functions – Properties
Laplace transform of periodic functions
Inverse Laplace transforms
Transform of derivatives and integrals
Unit step function (Heaviside function) –Dirac’s Delta function
Applications to solution of linear ordinary differential equations of second order with constant coefficients
Simultaneous linear equations with constant coefficients.
