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)
Triple Integration (Cartesian co-ordinates)
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
Divergence of a vector field – Curl of a vector field
Solenoidal and Irrotational of a vector
Problems based on Greens theorem.
Problems based on Gauss Divergence Theorem
Problems based on Stokes Theorem
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:
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
Inverse Laplace transforms
Applications to solution of linear ordinary differential equations of second order with constant coefficients
Laplace transform of periodic functions
Unit step function (Heaviside function)& Dirac’s Delta function
Simultaneous linear equations with constant coefficients