## 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 early September of 2020.

Brief overview of calculus

Average rate of change

Introduction to limits

Technical definition of limits

Squeeze Theorem; one-sided limits

Continuity

Limits with infinity; asymptotes

Derivative at a point; tangent lines

Derivative as a function

Rules for derivatives

Higher order derivatives with some applications

Derivatives of trigonometric functions

Chain rule

Implicit differentiation

Derivatives of inverse functions; logarithmic differentiation

Derivatives of inverse trigonometric functions

Related rates

Linearization and approximation

Critical points; extreme values

Mean value thoerem

Monotonicity; first derivative test

Concavity; second derivative test

Optimization

L' Hospital's rule

Newton's method

Antiderivatives

Areas and Riemann sums; sum notation

Area by limit of Riemann sum

Definite integrals

• Study guide

• Overview (video; scan)

• Practice (video; scan)

• More practice (video; scan)

Fundamental theorem of calculus

• Study guide

• Overview (video; scan)

• Practice (video; scan)

• More practice (video; scan)

Substitution and indefinite integrals

• Study guide

• Overview (video; scan)

• Practice (video; scan)

• More practice (video; scan)

Substitution and definite integrals; area

• Study guide

• Overview (video; scan)

• Practice (video; scan)

• More practice (video; scan)

Separable differential equations

• Study guide

• Overview (video; scan)

• Practice (video; scan)

• More practice (video; scan)

Logarithms as integrals; hyperbolic functions

• Study guide

• Overview (video; scan)

• Practice (video; scan)

• More practice (video; scan)