Online lectures

The following material corresponds with online materials prepared by Steve Butler. Most topics have a "clickable" PDF study guide which opens up the corresponding video. The topics will usually consist of a few sessions including an overview (which discusses the ideas and techniques) and some worked problem set(s). 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").

For best results the overview for a given topic should be reviewed and then work some subset of the problems (focus on basic problems first, and then more challenging as time allows). When needed the videos will provide a walk-through explanation of the solution.

The material is still under construction and should be completed soon.

Brief overview of calculus

Average rate of change [PDF]

Introduction to limits [PDF]

Technical definition of limits [PDF]

Squeeze Theorem; one-sided limits [PDF]

Continuity [PDF]

Limits with infinity; asymptotes [PDF]

Derivative at a point; tangent lines [PDF]

Derivative as a function [PDF]

Rules for derivatives [PDF]

Higher order derivatives with some applications [PDF]

Derivatives of trigonometric functions [PDF]

Chain rule [PDF]

Implicit differentiation [PDF]

Derivatives of inverse functions; logarithmic differentiation [PDF]

Derivatives of inverse trigonometric functions [PDF]

Related rates [PDF]

Linearization and approximation [PDF]

Critical points; extreme values [PDF]

Mean Value Theorem [PDF]

Monotonicity; first derivative test [PDF]

Concavity; second derivative test [PDF]

Optimization [PDF]

L'Hospital's Rule [PDF]

Newton's method [PDF]


Areas and Riemann sums; sum notation

Area by limit of Riemann sum