Back to Calculus: Single Variable Part 1 - Functions

4.8

1,042 ratings

•

269 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....

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.

Dec 16, 2016

Excellent class. Prof. Ghrist has a great teaching style, and his idea to use Taylor Series first is quite effective. Many functions I have shied away from in the past are now familiar to me.

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By Valerie C

•Mar 07, 2016

I found this course to be very helpful, challenging, informative, and well-made. There was obvious a lot of time and effort put into making the videos. I have a good amount of math experience, but I still found it challenging and interesting. I'm very happy to have found this resource.

By Anna S

•Jun 30, 2016

Good and difficult

By 张柏豪

•Oct 09, 2016

wonderful class, and i am looking forward to the next part.

By Yizhou H

•Apr 27, 2017

A pretty great lecturer makes a good impact on my own study in math.

By Lijia L

•Feb 27, 2017

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

By Maarten B

•Jun 20, 2017

A very inspiring course, especially with such an awsome professor

By Neysan

•Dec 21, 2016

Stellar

By Kumail H A H

•May 22, 2017

Excellent course! Prior exposure to Calculus (familiarity with a couple famous derivatives and integrals) is helpful, but you're sure to learn much more than that in this course. I have deepened my understanding of limits (not just the notion of a limit, but working out limits is now more intuitive to me) and stuff like l'hopital's rule seems logical now.

Starting with infinite series, with contrast to leaving it at the end, which is the standard in such courses, was brilliant!

Highly recommended!

By Jarrod K

•Nov 11, 2016

Fantastic applied mathematics course for students interested in engineering. Extremely challenging but amazingly rewarding.

By Фесенко Г Е

•May 20, 2017

Great course, thank you! Easy explanations for complecated math theorems is exactly what I wanted to see in online course.

By N B

•Nov 12, 2016

Great course to take

By Sachin M V

•Nov 01, 2016

Makes all basic clear

By Matthew A

•Oct 15, 2017

Great introduction to calculus/analysis. Covers a good range of functions and applications. Starting with Taylor series is an approach I hadn't seen much before, it worked well. Fantastic graphics and animation, they make for a rather cool pedagogical aid. Prof Grist's delivery is another plus, it's simply very good.

My only concern is in treatment of 'Big-O' notation, I feel that the link with limits is not spelled out and expanded upon as well as it might be. Then again, I may not have understood things correctly.

Anyway, overall a very good course. Highly recommended.

By 刘钦生

•Mar 31, 2017

It's so great!

By Omar H

•Mar 09, 2017

The perfect course for someone with the basic knowledge of calculus and doesn't want to spend much time on the boring basic concepts (I am grad. student and need some calculus review). It is a genius idea that this course started with convergence and Taylor series, it made my life easier and simplified so many other things. The only part that I struggled with was the big "O" notation part, I feel it needs more elaboration. Other than this, everything is great. Off to the next course !

By Keqin H

•Jun 13, 2018

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

By Shahen K

•Jun 30, 2016

One of the best courses I've ever taken.

By Cessna

•Apr 02, 2016

Would like to recommend without reservation! Perfect course!

By Hoagy C

•Sep 30, 2017

Very well explained, well set out, interesting concepts - highly recommended. Would have liked it if the 'Challenge' question sets were a little more thought provoking rather than (often) just requiring more computation - there were some interesting ones (the ln(lnx) question comes to mind) but didn't add as much depth as they could have.

By Khvan V A

•Apr 13, 2018

Super Course!

By Mengyun Z

•Jun 14, 2016

The lectures are delivered in a clear and straightforward manner. Videos do a good job in walking me through the key points related to the topic. And the exercises were well designed to capture the

By Patricia B

•Jul 11, 2017

Best calculus course ever.

By Wanying P

•May 11, 2017

Very good course and format, highly recommended!

By Adam J

•Feb 22, 2017

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

By 易灿

•May 16, 2016

Very intuitive, I think 1.5 speed is more properly