Real Analysis 52 | Riemann Integral - Examples

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This is my video series about Real Analysis. We talk about sequences, series, continuous functions, differentiable functions, and integral. I hope that it will help everyone who wants to learn about it.

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I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

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My Calculus I & II Professor (Tony Tromba, UC Santa Cruz, Fall 1981) dropped the Dirichlet Function on us at the end of a Friday lecture to give something to snack on during Happy Hour.

douglasstrother

This is almost the end in a real analysis course, what's the direction next? I have enjoyed this series very much rewatched a few episodes to remind me a few important points.

evionlast

Excellent explanation ! Thank you sir .

wtt

I'm taking a foundations of analysis course and I'm struggling to understand the content, so in searching I found your videos "among others, but yours being particularly enlightening". With that said, do you have a preferred textbook for learning real analysis that you could recommend? Your videos are helping me succeed as a better person, I honestly cant thank you enough Sir!

mr.petersen

Concerning the Riemann integral of the Dirichlet function, at 3:43 we have *“the rational points lie dense in the real number line”* (although this expression is not defined). Then at 4:25 we have *_“for any segment you choose on the real number line, you always find a rational number”._*

How are we to understand the above statement, when we also have the statements:
(1) the rational numbers are “countably infinite”
(2) the real numbers are “uncountably infinite",
given that an uncountable infinity is a much larger infinity than a countable infinity?

Leslie.Green_CEng_MIEE

Awesome Explanation!!!! Now i understand what my lecturer has been saying.
Thank you!

mathswithbuka

Final Exam Extra Credit Problem: Plot the Dirichlet Function. More points = more points!

douglasstrother

can u do multivariable calculus, partial Derivatives and Tangent Plane also plz

megavarshinim

first :) will you cover the riemann stieljes integral? (not sure if that was the correct spelling for steljes)

mastershooter

Hello, what software do you use for these videos?

ariuwu

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