Continuity and Differentiability

In this program students will first recapitulate the concept of limits which they have learned in their previous grade then slowly they move to this topic which is the heart of calculus In this program student will learn Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation. The main focus here to is make the student comfortable in calculus since it has a wide range of applications which will be used later on. All the topics are followed with the help of various assignments and homework.