Real number system and its properties, l.u.b., g.l.b. of sets of real numbers, limit of a function, Basic properties of limits. Continuous functions and classification of discontinuities. Uniform continuities, differentiation of hyperbolic functions. Successive differentiation. Leibnitz theorem. Taylor’s and Maclaurin’s theorem with various forms of remainders. Indeterminate forms.
De-Moivre’s theorem and its applications, circular and hyperbolic functions and their inverses. The exponential and logarithmic function of complex numbers, Expansion of trigonometric functions, Gregory’s series, Summation of series.