Complex Analysis: Roots of a complex number. Addition formulae for any number of angles. To express sine in series or cosines of multiple angles. Exponential function of a complex variable. Circular functions of complex

variable. Hyperbolic functions. Real and imaginary parts of circular and hyperbolic functions. Logarithmic functions of a complex variable. Real numbers; sequence and series; their convergence and divergence.

Vector: Force, moment and angular velocity. Vector differentiation and integration.

Linear Algebra: Linear spaces, algebra of determinants and matrices.

Calculus: Differentiations and applications. The mean value theorem and its applications. Extension of mean value theorem. Taylor and Maclauren formulae, Liebnitz’s theorem. (Application to the solution of differential equations with variable coefficients), de L’Hospital’s. Partial derivatives of functions of two and more variables.

- Lecturer: Rowland Azike