Properties of Real Numbers : Order property of real numbers, bounds, l.u.b. and g.l.b. order completeness property of real numbers, Archimedian property of real numbers.
Limits : e–d definition of the limit of a function, basic properties of limits, infinite limits, indeterminate forms.
Continuity : Continuous functions, types of discontinuities, continuity of composite functions, continuity of | f (x) |, sign of a function in a neighborhood of a point of continuity, intermediate value theorem, maximum and minimum value theorem.
Mean Value Theorems : Rolle’s Theorem, Lagrange’s mean value theorem, Cauchy’s mean value theorem, their geometric interpretation and applications, Taylor’s theorem, Maclaurin’s theorem with various form of remainders and their applications.
Hyperbolic, inverse hyperbolic functions of a real variable and their derivatives, successive differentiations, Leibnitz’s theorem.