Back to Calculus: Single Variable Part 1 - Functions

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1,690 ratings

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463 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 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.\n\nThank you so much Prof. Ghrist.

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By Hemant P

•Jul 1, 2017

This course really helped me push my limits(forgive the pun) with highschool math. It was challenging but not so much that it demotivated me! Moreover, I watched many lectures twice and thrice and tried replicating the examples demonstrated in each lecture. It really helped me drill in the fundamentals I needed. I can proudly say I know Taylor Series now!

By Nafis F

•Aug 8, 2020

For people with absolutely no knowledge of calculus : Quite difficult to follow. Not for you.

For people with absolutely some knowledge of calculus: TAKE THIS COURSE, if you have the time to do so. It does take a lot of work. But I enjoyed all of it.

By Макарова Ю А

•Apr 2, 2020

Very nice course. I've been searching for a calculus course for some time as I want to try a completely new sphere for me and I needed something just above school program, but also not too advances as I graduated from school 10 years ago and don't remember everything. I am really grateful for these lectures and tasks, it was actually fun. Thank you!

By Hoagy C

•Sep 29, 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 Emmanuel A

•Dec 9, 2020

I have really enjoyed this course; calculus with UPenn is the best. Thank you a lot especially to Professor Robert Ghrist. I appreciate your teachings and everything you did for me. Infact, I have really understood the practical aspect of mathematics. To all my coursera friends, you're at the right place with University of Pennsylvania.

By Darleen J T S

•May 17, 2020

A very useful course to reinforce and measure your knowledge of simple variable calculus at the level of functions, limits and Taylor series. I especially thank the teacher R. Ghrist and his collaborators for the didactic material that they have given us as well as for the challenging problems that they have posed to solve.

By Patrick S H

•Oct 5, 2019

I really appreciate the work that Professor Ghrist and the online curriculum team have put into making classes like this so accessible. I didn't feel like I was up to my knees in spam-can explanations, and just left to my own devices. Professor Ghrist is actually a very good tour guide for some very interesting territory.

By Bowei D

•Nov 30, 2020

In my class of my university, series number is always set up at the end of the arithmetic course, and I dont have the opportunity to combine series number with derivative and integral, also its amazing to learn something about the order of the point, it can be applied in many situation that I never consider before.

By Okto T

•Dec 20, 2019

Amazing course, taught by a brilliant professor. A very useful course for me, as my previous calculus experience did not include Taylor Series. The homework took me a lot of time though, always over an hour. I didn't always manage the challenge homework. Overall very satisfied and looking forward to the next part.

By Alperen Ç K

•Sep 5, 2020

Very well organized course with clear explanations. Plenty of visual slides which makes understanding better. Professor is also focusing on many details that normally requires proper explanation and he does explain those details clearly. The focus is on the Taylor Series. I can't wait to finish other parts!

By Shaurya A

•Jun 4, 2020

Course overall was great. The Professor Robert Greist explained wonderfully and the animation was also great. But there was a gap in the understanding about the big O and asymptotics specifically in week 4 lecture : Orders of growth

But everything else went in a great flow.

Looking forward to calculus 2

By Brian N A

•Jun 24, 2018

I enjoyed the course, and I will be taking the other parts of it too. The problems seem well designed to expose flaws in your thinking. I still feel somewhat shaky on some topics, but I would say the overall concepts came through very well, and the journey through them was cohesive and well laid-out.

By Deleted A

•Apr 30, 2020

I really loved it, to be honest. I am a high school student, and, I had some exposure to calc before, but, when I took this course, I got bombed on the first attempts lol. It was really tough and this has been my first ever course which really tests my brain. Honestly, I have learnt a lot of stuff.

By Mikayla B

•Jun 18, 2016

This course offers so much! I haven't been in a class that goes this in-depth in calculus. I definitely recommend this course to others who want to explore calculus and want a challenge!

Best of luck to those who choose to enroll in all 5 parts of single variable calculus sessions. It's worth it :)

By Carlos A

•May 2, 2017

It was great, the lectures were amazingly done, I loved all the colors and stuff made.

Clear and understandable.

Exercises not too hard, not too easy.

Our starting point is Euler's identity and Taylor Series, wich we take as a given. I didn't like it very much, but, overall, it accomplishes its goal.

By Don H

•Mar 2, 2019

It's not perfect, but no course is. This course won't raise your test scores (at least not immediately). To do that, you have to buckle down and study the material assigned by your professor. But if you want a deeper understanding of the concept, I couldn't recommend a better course or platform.

By michael f

•May 18, 2017

I thoroughly enjoyed this course. Prof. Ghrist is an excellent teacher. The course was a tad bit harder than i has expected it to be, but nonetheless, i thoroughly enjoyed it and would recommend it to anyone who has an interest in Mathematics and calculus. It also cleared some of my concepts.

By Alejandro C

•Mar 8, 2021

Really good course! Calculus has always been a hard bone to chew for me, but this helped a lot. The only part that is a little bit lacking was the complex exponential, luckily I had recently seen some videos on the subject in the 3b1b youtube channel that complemented this lecture perfectly.

By Valerie C

•Mar 6, 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 Meysam N

•May 9, 2021

It is a little bit difficult to follow the course since it is not clear what are the learning objectives. However, once I insisted on following the material and forcing myself into it I had the opportunity to learn so many beautiful concepts that were totally new to me in mathematics.

By Kannadasan P S

•Jul 15, 2020

Got to know to some of the crucial concepts like Big-O which was a base for complex computation in the calculation of time for programmes. And the lectures were very interesting as they were explained with application. The overall feel while learning the course was good !!

By Aleksey C

•Dec 29, 2016

When I retake homework tasks I try to fix tasks I failed on previous attempt. IMHO it make sense to not repeat them all but provide only tasks that were solved incorrectly. Repeating ALL tasks just wastes my time for reentering correct answers and is error-prone process.

By Ross L

•Nov 26, 2018

This is a much more in-depth calc class than I've had at univ, and by more in-depth I mean it's harder. That being said I feel like I understand the material better as before there was much more memorization whereas this has more explanation. A++++++ would take again.

By Pedro R

•Dec 26, 2018

It's a very good course that uses a different point of view to understand how things works in calculus. It's very didatic and helps you think outside the box. If you're thinking about do the course, keep in mind that it is necessary previous knowledge in calculus.

By ZIXIANG Y

•Jun 17, 2018

I would highly recommend this course to those who are trying hard to study calculus in Chinese universities but having a hard time understanding calculus. After finishing this course, you will find it useful to use Taylor Expansion to solve limit problems in tests.

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