Back to Calculus: Single Variable Part 1 - Functions

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2,195 ratings

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 2, 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.

NL

Feb 9, 2021

Excellent introduction to Calculus, I wanted to review the material to tutor my child but I am very happy that I learned a whole new way of looking at Calculus.

Thank you so much Prof. Ghrist.

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By Vashurin R

•Apr 25, 2016

Course is really cool, but oriented mostly on practical exercises and providing definitions. It would be much better if it had more formal proofs. Otherwise excellent course with a lot of challenging problems to solve.

By Daniel

•Jul 26, 2020

It is a really good course, with a lot of definitions used at undergraduate level and well explained. Nevertheless, I could not understand too much about Big O. Probably, more examples would be useful to clarify it.

By Nisarg K

•Feb 23, 2016

Would have preferred accompanying solutions. Just getting the answer ain't enough. Making sure my approach is correct is essential as well considering the course touches upon the absolute basics.

By Yusuf F

•Sep 20, 2020

There were certain advanced concepts that could have had a better and clearer explanation such as the “big O”. But on the whole it was a very good course and very much recommendable.

By a l s

•Jul 14, 2017

The course is intriguing. More practice questions and explanations will be good. And it will be beneficial if it can provide extra background knowledge (or link) for further study.

By Aditya T

•Aug 14, 2020

Very insightful. However, I believe (although I may be wrong) that certain methods and techniques required to solve the homework problems weren't explained in the course material.

By Oscar K

•Jul 25, 2021

Really enjoyable and well thought out explanations, but many examples went unexplained which I consider a waste since it would be useful to see the thought process of a solution.

By Francisco A

•Jun 7, 2020

I quite enjoyed the course, although I found it unnecessarily tough sometimes. I believe extra solved examples for convergence, geometric and binomial series could help a lot!

By Mount

•Sep 4, 2016

ppt真心做得很漂亮，但是这门课程不是一门入门课，面向对象是在已经掌握了微积分的前提下、希望对微积分进一步了解和巩固的学生，自然，有些地方的讲述是非常仓促的。

思路上讲主线一直围绕泰勒级数展开，也总是以泰勒级数为思考角度（包括后面part 2也是如此），个人并不是十分适应这种纯数学的方式，更喜欢感官上、性质上来把握，所以……仁者见仁智者见智吧 ^_^

By Krishna P R

•Jun 20, 2018

I have taken a calculus course at university which dealt with the epsilon-delta definition of things. Enjoyed the different approach as well, keep up the good work!

By Benjamin C

•Mar 19, 2018

Challenging, because begins with the infinite series, which are not a simple concept. Once complete, a much higher level of mathematical understanding is achieved.

By Ohedul I

•Sep 27, 2022

Its a very nice course for calculus, serise and function. Videos could be more descriptive with examples. Homeworks are nicely designed to cover the whole topic.

By Jules G

•May 4, 2022

good instructions and relevant exercises! The course could just improve the explanation for big O since I had to research some more apart to understand it better.

By Harshini s

•Jun 29, 2020

The order of growth lecture is extremely unclear and lacks sufficient information. Tt can be made more elaborate and a couple more examples would really help.

By Anna G

•Aug 7, 2017

A good course but quire difficult and definitely requires a strong calculus foundation. The weird rhythm of the professor speaking is somewhat distracting.

By Alexander O

•May 11, 2020

High quality and entertaining videos. Correcting some organizational mistakes (like current links to textbook) would make this a five star class.

By Michelle R

•Oct 7, 2022

It would be more effective if given real example not abstract and more effective again if detailed. But despite this, it is challenging one.

By HAIBO W

•Aug 16, 2020

The course explains the knowledge quite clearly, but it is not really easy. The Quizzes can have some more tips as that would help me think.

By Dr. T V R

•Dec 27, 2016

I would like to have been able to review some quiz questions with answers after the course was complete. That option does not seem to exist.

By Gloria M

•Sep 27, 2020

this is a good way of reviewing calculus . the part of functions was not that much hard as Prof Ghrist keep saying it just need commitment

By Harsha V

•Feb 26, 2018

The lectures on Big O (growth rates) are way too hard to comprehend, compared to the rest of the lectures. Please do try to simplify them.

By Ayanabha P

•Jul 20, 2020

It was a nice course. Learned quite a bit about calculus. slides designes was awesome. love to complete other courses by prof. ghriest.

By Calvin l

•Jan 1, 2024

I liked it, a more unconventional start for calculus. First time with Big-O notation. Instructor feels AI generated though LOL

By Ehsanul H R

•May 31, 2020

This is a very good course to understand the main theme of calculus. Though it was little bit hard I enjoyed the course.

By Jorge C

•Mar 18, 2020

Sometimes explanations are not complete enough to understand the problems. However, in general terms is a great course.