First-Year Calculus Videos

These videos cover concepts from the first-year Calculus syllabus, explained through the use of examples by faculty members of the Mathematical and Computational Sciences Department.

Students from the department helped in the creation of the videos. Funding was provided by the department, the Provost’s Instructional Technology Innovation Fund, the University of Toronto and the Office of the Dean at the University of Toronto Mississauga.

We hope you find these videos useful.

All YouTube MCS Math Videos

The Limit of a Function



Horizontal and Vertical Asymptotes

Horizontal and Vertical Asymptotes

Basic Differentiation

The Derivative

The Derivative

The Chain Rule

Implicit Differentiation and Logarithms

Related Rates

L'Hopital's Rule

Concavity and Inflection Points 

Optimization Problems in One Variable

Optimization Problems in One Variable


The Definite Integrral and Riemann Sums

The Fundamental Theorem of Calculus

Calculating Areas

The Substitution Method

Integration by Parts

Improper Integrals on Unbounded Intervals

Improper Integrals on Bounded Intervals

Trigonometrics Substitution

Integration by Partial Fractions