UNIT 1:
Derivatives: Gradient and Directional Derivative
Divergence & Curl of a vector field
Solenoidal and Irrotational of a vector
Problems based on Green’s theorem
Problems based on Gauss Divergence theorem
Stoke’s theorem with problems
Application in evaluating line, surface and volume integrals.
UNIT 2:
Higher order linear differential equations with constant coefficients
Problems based on higher order linear differential equations with constant coefficients
Problems based on higher order linear differential equations with constant coefficients
Method of variation of parameters
Method of variation of parameters
Homogeneous equation of Euler’s type
Homogeneous equation of Legendre’s type
UNIT 3:
Derivatives of f(z) - Analytic function
Construction of Analytic functions
Mapping by functions w = c+z, w = cz , w = 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 & Singularities of an analytic function
UNIT 5:
Definitions, properties, existence conditions
Definitions, properties, existence conditions
Transforms of derivatives and integrals
Laplace transform of periodic functions
Initial and final value theorem
Inverse Laplace transforms
Solution of linear second order ordinary differential equations with constant coefficients
Solution of linear second order ordinary differential equations with constant coefficients
