**Complex Variables :** Definition, Cartesian,
polar & amplitude ; exponential form. de moivres theorem. power & amp;
roots of exponential and trigonometric forms. hyperbolic and logarithmic
functions. inverse hyperbolic and inverse trigonometric of all types of
functions.

**Vector Algebra :** Triple Product, Vector
Differentiation, Curvature and Torsion, Equation of planes.

**Calculus :** Successive differentiation, std
form to find the nth derivative, Leibnitz theorem, Rolles theorem ,Lagranges and
Cauchys mean value theorem, Taylors theorem, Taylor and Maclaurins series,
indeterminate forms, Lhospitals rule, expansion of functions in power series,
partial derivatives of first and higher orders, total differentiation concept of
commutative partial derivatives, Eulers theorems of homogeneous functions,
deduction from Eulers theorems ,errors, approximations, maxima and minima
functions of two variables.