Description
Real Numbers: Order properties of real numbers, bounds, l.u.b. and g.l.b., order completeness property of real numbers, Archimedean property of real numbers.
Limits: Functions (exponential, logarithmic, modulus, trigonometric, polynomials etc.), e – d definition of the limit of a function, basic properties of limits, methods of computations, infinite limits.
Continuity: e – d definition of a continuous function, various methods to check continuity/discontinuity of a function types of discontinuities, continuity of composite functions, sign of a function in a neighborhood of a point of continuity, intermediate value theorem, maximum and minimum value theorem.
Differentiability: Definition of a differentiable real valued function of a real variable, computing derivatives of elementary functions by using definition, Geometrical meaning of derivative of a function at a point,
Derivatives: Revision of various rules to compute derivatives (e.g. product rule, quotient rule, chain rule etc.), Introduction to hyperbolic, inverse hyperbolic functions of a real variable, their derivatives, successive differentiations, Leibnitz’s theorem, indeterminate forms.
Applications of Derivatives : Tangents and normals, Differentials and Approx./Errors.
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 forms of remainders and their applications.
