Functions

  1. Real-valued functions of a real variable, into, onto and one-to-one functions.

  2. Sum, difference, product, and quotient of two functions.

  3. Composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.

  4. Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions.


Limits and Continuity

  1. Limit and continuity of a function.

  2. Limit and continuity of the sum, difference, product and quotient of two functions.

  3. L’Hospital rule of evaluation of limits of functions.


Derivatives

  1. The derivative of a function, the derivative of the sum, difference, product and quotient of two functions.

  2. Chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.

  3. Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative.

  4. Tangents and normals, increasing and decreasing functions, maximum and minimum values of a function.

  5. Rolle’s Theorem and Lagrange’s Mean Value Theorem.