In-person lectures (Spring 2020)

The following material corresponds with in-person lectures given by Steve Butler during the Spring 2020 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").

Due to transitioning online the semester was shortened by one week (course reviews were cut); the lectures after the second exam were not recorded in front of students.

Review of differential and integral calculus

Integration by parts

Integration of trigonometric functions

Trigonometric substitution

Partial fractions

Numerical integration

Error estimation for numerical integration

Improper integration

Additional practice for integration

Q&A for Exam 1

Volume by cross sections; disc and washer methods

Volume by shell method

Arc length

Surface area of revolution

Additional practice for geometric applications

Work and fluid pressure

Mass and center of mass

Parameterized curves

Arc length and surface area for parameterized curves

Polar coordinates

Graphing in polar coordinates

Area in polar coordinates

Lengths in polar coordinates

Q&A for Exam 2



Integral test for convergence

Comparison tests for convergence

Ratio and root tests for convergence

Additional practice for convergence tests

Alternating series; absolute vs conditional convergence

Power series; radius of convergence

Additional practice with the radius of convergence

Taylor polynomials; Taylor series

Convergence of Taylor series; error estimates

Binomial series

Applications of Taylor polynomials

Q&A for Exam 3