Sergei Yakovenko's blog: on Math and Teaching

Sunday, December 27, 2015

Lecture 9, Dec 22, 2015

Integral and antiderivative

  1. Area under the graph as a paradigm
  2. Definitions (upper and lower sums, integrability).
  3. Integrability of continuous functions.
  4. Newton-Leibniz formula: integral and antiderivative.
  5. Elementary rules of antiderivation (linearity, anti-Leibniz rule of “integration by parts”).
  6. Anti-chain rule, change of variables in the integral and its geometric meaning.
  7. Riemann–Stieltjes integral and change of variables in it.
  8. Integrability of discontinuous functions.

Not covered in the class: Lebesgue theorem and motivations for transition from Riemann to the Lebesgue integral.

The sketchy notes are available here.

Advertisements

1 Comment »

  1. Thanks. It’s a nice post about integral antiderivative. I really like it :). It’s really helpful. Good job.

    Comment by Deepak Suwalka — Thursday, March 23, 2017 @ 1:48 | Reply


RSS feed for comments on this post. TrackBack URI

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Blog at WordPress.com.

%d bloggers like this: