Fall 2020 Online videos with steve butler

For each topic there are videos and scanned in notes. "Study guides" are linked to the videos so that clicking on any part of the study guide goes directly to that portion of the video.

These videos are currently in the process of being produced and are scheduled to be completed by October of 2020.

Brief overview of calculus

Introduction to applications of integration

Volumes by cross sections; disc/washer method

Volumes by shell method

Arc length

Surface area

Work and force

Mass and center of mass

Parametric curves

Applications with parametric curves

Polar coordinate system

Sketching and tangent lines with polar curves

Area with polar curves

Arc length with polar curves

Introduction to techniques of integration

Integration by parts

Trigonometric integrals

Trigonometric substitution

Partial fractions

Numerical integration (trapezoid rule; Simpson's rule)

Error analysis for numerical integration

Improper integrals (definite integrals involving infinity)

Introduction to sequences and series

Sequences

Series (geometric/telescoping)

Integral test; basic divergence test

Comparison tests

Root/ratio tests

Alternating series test; absolute vs conditional convergence