B.Sc.Nautical Science

Contents of the course comprises of

Complex Variables
Definition, Cartesian, Polar & exponential form. De-Moivre's Theorem. Power &
Roots of Exponential and Trigonometric Functions.
Hyperbolic & Logarithmic Functions. Inverse Hyperbolic & Inverse Trigonometric
Functions. Separation into real and imaginary parts of all types of functions.

Vector Algebra and Calculus
Scalar and Vector Triple Products. Differentiation of a vector function of a single
scalar variable. Derivative of a unit vector, application to curves in space, principal
triad, Sennet-Frenet form.

Differential Calculus
Successive differentiation. Standard form to find the nth derivative. Leibnitz's
theorem, Rolle's theorem (with proof), Lagrange's and Cauchy's mean value
theorem (with proof), Taylor's theorem, Taylor's and Maclaurin's series (without
proof). Indeterminate forms, L'Hospital's rule, Expansion of function in power series
(all types), Partial derivatives of first and higher orders.
Total differential, Concept of commutativity of partial derivatives (without proof).
Euler's theorem on homogeneous functions. Deduction from Euler theorems.
Errors & approximations. Maxima & minima of the functions of two variables.