UNIT 1:
Problems on Area enclosed by plane of curves
Double Integration in Cartesian coordinates
Change of order of integration
Problems on Change of order of integration
Area enclosed by plane of curves
Problems on Triple integrals
Problems on Volume of solids
UNIT 2:
Divergence of a Vector field, Curl of a vector field
Introduction of vector operations, Gradient , Directional derivatives
Solenoidal , irrotational of a vector
Greens theorem and Applications
Problems in Greens theorem
Gauss divergence theorem and Applications
Problems in Gauss divergence theorem.
Stokes theorem and Applications
Problems in Stokes theorem
UNIT 3:
Introduction to complex variables, Derivative of f(z) and analytic functions and CR equations
Harmonic function and Harmonic conjugate
Construction of Analytic functions
Problems based on construction of analytic functions
Problems based on conformal mapping w = z+c ,cz
Problems based on conformal mapping w=1/z,
Problems based on Mobius transformation
Application to flow problems
Problems based on conformal mapping w = z+c ,cz
UNIT 4:
Introduction to complex integration ,Cauchy’s integral theorem
Cauchy’s integral formula
Problems based on Laurent’s series
Cauchy’s integral formula
UNIT 5:
Introduction to Laplace transforms and transforms of elementary functions
Properties of Laplace transform
Derivatives of Transforms
Integrals of Transforms, Transform of unit step function and impulse function
Transform of Periodic functions
Inverse Laplace transforms
Problems in convolution theorem
Solution of linear ODE of 2nd order by using Laplace Transform
Introduction to Laplace transforms and transforms of elementary functions
Transform of Periodic functions
