UNIT 1:
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 Area enclosed by plane of curves
Problems on Triple integrals
Problems on Volume of solids
UNIT 2:
Introduction of vector operations, Gradient , Directional derivatives
Divergence of a Vector field, Curl of a vector field
Solenoidal , irrotational of a vector
Greens theorem and Applications
Problems in Gauss divergence 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 = z+c ,cz
Problems based on Mobius transformation
Problems based on conformal mapping w=1/z,
UNIT 4:
Introduction to complex integration ,Cauchy’s integral theorem
Cauchy’s integral formula
Problems based on Laurent’s series
Problems on Cauchy Residue theorem
UNIT 5:
Introduction to Laplace transforms and transforms of elementary functions
Integrals of Transforms, Transform of unit step function and impulse function
Properties of Laplace transform
Derivatives of Transforms
Inverse Laplace transforms
Inverse Laplace transforms
Solution of linear ODE of 2nd order by using Laplace Transform
Problems in convolution theorem