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

All YouTube MCS Math Videos

The Limit of a Function

The Limit of a Function

Continuity     

Continuity

Horizontal and Vertical Asymptotes

Horizontal and Vertical Asymptotes

Basic Differentiation

Basic Differentiation

The Derivative

The Derivative

The Chain Rule

The Chain Rule

Implicit Differentiation and Logarithms

Implicit Differentiation and LogarithmsI

Related Rates

Related Rates

L'Hopital's Rule

L'Hopital's Rule

Concavity and Inflection Points

Concavity and Inflection Points

Optimization Problems in One Variable

Optimization Problems in One Variable

Antiderivatives

Antiderivatives

The Definite Integral and Riemann Sums

The Definite Integral and Riemann Sums

The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

Calculating Areas

Calculating Areas

The Substitution Method

The Substitution Method

Integration by Parts

Integration by Parts

Improper Integrals on Unbounded Intervals

Improper Integrals on Unbounded Intervals

Improper Integrals on Bounded Intervals

Improper Integrals on Bounded Intervals

Trigonometric  Substitution

Trigonometric Substitution

Integration by Partial Fractions

Integration by Partial Fractions