Continuity   Definition, continuity of a function at a point and on a domain. Examples and problems, Algebra of continuous functions, problems , continuity of composite function and problems
Differentiability Defining logarithm and mentioning  its properties , Concepts of exponential, logarithmic functions, Derivative of ex , log x from first principles,
  Derivative of composite functions using   chain rule,  problems.
  Derivatives of inverse trigonometric functions, problems.
  Derivative of implicit function and problems.
  Logarithmic differentiation and problems . Derivative of functions expressed in parametric forms and problems.
  Second order derivatives and problems
  Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric Interpretations and problems