Calculus Revisited: Single Variable Calculus

Part II: Differentiation

In this part of our course, we introduce the concept of instantaneous rates of change. At the pre-calculus level, the study of constant and average rates of change are introduced as early as elementary school when students start working with fractions. However, in many real-life applications (such as the speed at which an automobile travels), rates are not constant and it becomes important to study instantaneous rates of change. Differential calculus is the branch of mathematics that deals with this topic.

Lecture 1: Derivatives of Some Simple Functions

Lecture 2: Approximations and Infinitesimals

Lecture 3: Composite Functions and the Chain Rule

Lecture 4: Differentiation of Inverse Functions

Lecture 5: Implicit Differentiation

Lecture 6: Continuity

Lecture 7: Curve Plotting

Lecture 8: Maxima and Minima

Lecture 9: Rolle's Theorem and its Consequences

Lecture 10: Inverse Differentiation

Lecture 11: The "Definite" Indefinite Integral