Limits, Continuity and, differentiability: Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions. Continuity and differentiability
Unit II:
II
9.00
Differentiation: differentiation of functions: polynomial, trigonometric, logarithmic and exponential functions, derivative of composite functions, chain rule, Derivative of functions expressed in parametric forms, Second order derivatives.
Unit III:
III
9.00
Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as in real life situations).
Unit IV:
IV
9.00
Integration as an inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions, and by parts, Evaluation of some elementary integral problems based on them.
Unit V:
V
9.00
Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
