In-person lectures (Fall 2019)

The following material corresponds with in-person lectures given by Steve Butler during the Fall 2019 semester. Each session has a scanned in copy of the notes ("PDF") and is available in streaming from two different online platforms (either "Vimeo" or "YouTube").

Rates of change and tangents

Limits of a functions and basics of limits

One-sided limits; Squeeze


Limits involving infinity

More practice with limits

Tangents and derivatives at a point

Derivative as a function

Differentiation rules

More practice with differentiation rules

Derivative as a rate of change

Derivative of trigonometric functions

More practice with using derivatives

Chain rule

More practice with the chain rule

Q&A for Exam 1

Implicit differentiation

Derivatives of inverse functions and logarithms

Inverse trigonometric functions

Related rates

Linearization and differentials

Extreme values

Mean value theorem

Monotonicity; first derivative test

Concavity; second derivative test

L'Hospital's rule


More practice with optimization

Newton'e method

Q&A for Exam 2


Areas and Riemann sums

Sum notation and limits of sums

Definite integrals

Fundamental theorem of calculus

Indefinite integrals and substitution

Definite integrals and substitutions; area

Q&A for Exam 3

Separable differential equations

Logarithm as an integral; hyperbolic functions

Course overview