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

Introduction to applications of integration

Volumes by cross sections; disc/washer method [PDF]

Volumes by shell method [PDF]

Arc length [PDF]

Surface area [PDF]

Work and force [PDF]

Mass and center of mass [PDF]

Parametric curves [PDF]

Applications with parametric curves [PDF]

Polar coordinate system [PDF]

Sketching and tangent lines with polar curves [PDF]

Area with polar curves [PDF]

Arc length with polar curves [PDF]

Introduction to techniques of integration

Integration by parts [PDF]

Trigonometric integrals [PDF]

Trigonometric substitution [PDF]

Partial fractions [PDF]

Numerical integration (trapezoid rule; Simpson's rule) [PDF]

Error analysis for numerical integration [PDF]

Improper integrals (definite integrals involving infinity) [PDF]

Introduction to sequences and series

Sequences [PDF]

Series (geometric and telescoping) [PDF]

Integral test; basic divergence test [PDF]

Comparison tests

Root and ratio tests

Alternating series test; absolute vs conditional convergence