Complex integration, line integral of real functions, line integral of complex functions, contour integrals (SUBJECT CVT)

 

Application Problems of Harmonic Functions (Electrostatic problems, potential function, stream function, irrotational fluid problems)

 

Derivative of complex function in Polar form, Orthogonal Curves, Harmonic Functions, Conjugate Harmonic functions, Laplace Equations

 

Analytic Functions, CR-equations (Cauchy Riemann Equations) in Cartesian and Polar Coordinates systems, Regular Function, Entire Function, Singular points, Derivative of a Complex Function using Partial Derivatives

 

Complex Variables, Complex Functions, Limit of Functions of a Complex Variable, Continuity of a Function of a Complex Variable, Differentiability of a Function of a Complex Variable, Theorem: (Existence of a Finite derivative)

 

Complex Functions, Single-Valued and Multi-valued Complex Functions, Types of Complex Functions (Circular Functions, Exponential Functions, Hyperbolic Functions, Logarithmic Functions, Inverse Trigonometric Functions, Inverse Hyperbolic Functions), Euler's Identities, Complex Powers

 

Polar Form of Complex Numbers, Argand's Diagram, Product and Quotient Rule For Polar Form of Complex Numbers, DE-MOIVRE'S THEOREM