Back to Calculus: Single Variable Part 1 - Functions

4.7

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1,514 ratings

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404 reviews

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.
In this first part--part one of five--you will extend your understanding of Taylor series, review limits, learn the *why* behind l'Hopital's rule, and, most importantly, learn a new language for describing growth and decay of functions: the BIG O....

YG

Jul 03, 2018

Very well structured for a refresher course. Thank you Professor Ghrist for your effort in putting this course together. A little additional outside research was required but well worth the effort.

KR

Aug 18, 2020

Very good and challenging material! This motivated me to do better in my Calculus Courses. Would definitely have more of these courses soon, as this is suited for higher mathematics in college.

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By Xiyang S

•Mar 19, 2019

Great course series to learn, thanks for the work of the staff! Hope to study Multi Variable series soon.

By Keqin H

•Jun 13, 2018

Extremely concise lectures. Good aiding graphics. The HWs are challenging yet doable. Highly recommended.

By Maksym S

•Mar 31, 2020

Very good video lecture. Very good speech for not native english students. But little difficult for me.

By Pavel K

•Jun 16, 2019

Good explanation of quite complicated things. Bonus materials are especially useful for understanding.

By Florent C

•Jun 15, 2020

Excellent course, although the wiki is currently broken and can only be accessed through archive.org.

By Xiaolin H

•Feb 09, 2018

Wonderful lectures! Clear and succint! It would be greater if more application examples are involved.

By Eva N

•Nov 19, 2019

This was very useful. Explanations were (relatively) simple and the quiz commesurate to the teaching

By Omar J

•Sep 29, 2018

A very challenging course that makes the quizzes and challenges sweet and passing it even sweeter!

By Rep G

•Feb 15, 2020

Growth of functions approach is somewhat more effective tool for reasoning than the normal stuff.

By John H

•Dec 21, 2019

Great course. Really good videos and the exercises seem to be at a really good level. Thank you.

By Adam O

•Mar 29, 2017

This was very explanatory and helpful. I would recommend it to many of my friends and colleagues.

By Adam J

•Feb 22, 2017

Professor Ghrist is a badass. Re-ordering things to put Taylor series first is a brilliant idea!

By Nesrine Z

•Apr 10, 2020

I really enjoyed the course, it was very helpful to understand the Taylor series. Many thanks.

By Lijia L

•Feb 27, 2017

I like this course very much. Prof. Robert Ghrist is humorous, and the mentor is very helpful!

By Jiaming L

•Aug 26, 2019

The course is perfect and the professor put all his effort on the program. It did help a lot.

By faraz g

•Apr 30, 2020

It was really useful. But, the tests were very hard. I did enjoy this course. Thank you all.

By Sabhrant S

•Apr 07, 2020

I liked the difficulty of the questions. Very good course. Thank you sir for your hard work.

By CMC

•Jun 26, 2018

The course is rigorous. I managed to learn something about Big-O that I did not know before.

By 黎健钊

•May 01, 2017

learn a lot about calculus which is different from China Calculus Book, Thank you so much...

By Jerry M

•Dec 26, 2016

This is an excellent course! I enjoyed the problem sets and the Bonus Lectures. Well Done!

By Carlos A G R

•Jul 08, 2020

Excellent course. Thank you very much for providing this course. And for sharing knowledge

By Zhu L

•Aug 19, 2018

This is an excellent course, thank you professor, your analysis process helps me a lot!

By Huang-Yu C

•Mar 22, 2018

I learn a lot by participating in the class! Thank you professor~ and also thanks UPenn

By Jair R

•Jul 10, 2020

This is an exceptional course. I learned about Calculus from another perspective here.

By Ian C

•Apr 14, 2020

I didn't have the time to complete it, but this is an excellent and worthwhile course

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