Functions of One Real Variable

Limit

Continuity

Intermediate value property

Differentiation

Rolle’s Theorem

Mean value theorem

L'Hospital rule

Taylor's theorem

Maxima and minima

Lecture 1: What is a function?

Lecture 2: min-max theorem for continuous functions.

Lecture 3: Local and Global extreme values.

Lecture 4: First derivative theorem for local extreme values.

Lecture 5: Problems on finding extreme values of functions.

Lecture 6: All critical and boundary points may not be the points of local extreme values.

Lecture 7: How to find out if a critical/boundary point is a point of local extreme value?

Lecture 8: Problems on finding extreme values revisited

Lecture 9: Rolle’s theorem

Lecture 10: The mean value theorem

Lecture 11: Concave up and concave down graphs

Lecture 12: Point of inflection

Lecture 13: Cartesian graphing using first and second derivatives I

Lecture 14: Cartesian graphing using first and second derivatives-II

Lecture 15: Cartesian graphing using first and second derivatives-III