Back to Calculus: Single Variable Part 1 - Functions

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2,194 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 Christian V

â€¢Oct 7, 2023

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By Joao M d C

â€¢Jun 9, 2021

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By æ´ªå•¸å®‡

â€¢Jun 19, 2016

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By helena r

â€¢Apr 14, 2020

The course is *incredibly* difficult, there's no getting around that. I walked into the course with prior exposure to calculus and even did well on the diagnostic test, and I'm here to tell you: it is HARD. That being said, it is rewarding and my knowledge of calculus was expanded way beyond what I learned in high school. The only reason I'm giving the course 4 stars instead of 5 is because 1- the lectures are very short and don't go into extensive detail. I'm sure this is fine for a lot of people, but for me personally I usually like to go into a lot of depth when it comes to math because that helps me understand what I'm doing and why I'm doing it. You're for sure going to need to use outside sources like Khan Academy if you need anything within the course expanded on. Overall, I'd recommend the course if you need to widen your calculus knowledge and if you're looking for a challenge.

By hamid m

â€¢Dec 26, 2020

it was a great class. i'm glad that i took it. i would recommend it

it was rather abstract; the problems were complicated and involved, emphasizing calculation rather than theory. the course has a narrow and limited focus

i realize the traditional route (calc 1, calc 2, calc 3, etc), however, there is another calc 1 class that was offered before this one that was completely different - different topics and emphasis on different subject matter. i would rather be able to take them both. i would like to take calc 1, this version, & calc 1, previous version. i don't see why the previous calc 1 class was replaced by this one

By Carlene S d F

â€¢Apr 26, 2021

The Course is only worthwhile if you already have a sense of Calculus. I did not think that the material provided was sufficient to solve the problems of the course. Even though I already had exposure to Calculus and mathematical physics, I found some exercises quite difficult. If you are not from the hard sciences, this course may not be the most suitable. Khan Academy is more introductory. But at the beginning of the course, there is a placement test to find out if the person is able or not to start the module. This can serve as a basis if the person has mastered the necessary prior knowledge.

By Rob G

â€¢Oct 5, 2020

Some areas could use some review perhaps a pre-calculus- pre part 1. More worked examples would be nice. The worked examples could perhaps be provided as supplemental reading for those of us who could use the extra practice so these concepts really sink in. Finally i am still confused about Big O. I understand the concept well enough but needed more explanation when using the example functions. This seems like a topic that is not included in Calculus often so i am having trouble finding supplemental material. Thanks for putting this out to the public though!!

By Robert B M

â€¢Feb 19, 2020

I genuinely enjoyed this course, which was more of a refresher for me, having taken several units of calculus for my undergraduate degree. The way in which the utility of the Taylor series was brought out was particularly interesting. The topics covering orders of growth & asymptotics, while familiar, were the parts I found most challenging. It might be nice in future iterations of the course if there were a discussion on graphs of the functions of interest alongside the topics covering orders of growth and asymptotics. All in all a great course!

By Gabriela M F

â€¢Sep 12, 2020

Before all, sorry about my english. I really enjoyed this course, and of course, I will get (if its possible) the following ones. I have a few difficuluts in some items. For example, I don not write using latex code, I think i will repass it. And, I can not read all the references in the forums. The most interesting was Penn Calc Wiki. I read some useful hings, but I can not read any example.

I only use the forums for reading other questions and answers, I was afraid of asking, but I think they are very useful.

Thans again for the oportunity

By Justin L

â€¢May 8, 2021

It was good but challenging. The only reason I only gave it 4 stars and not 5 is that I felt that some things could have been given a little more explanation, and also I feel that you will want to be reasonably comfortable with calculus already. For me, it has been 30+ years since I studied any calculus formally, and so a lot of the calculations and work was hard, as it was assumed knowledge. But these limitations or issues aside, the professor is a good teacher, and whilst I was thrown in the deep end, I gained and learned quite a lot.

By Seb M

â€¢Sep 11, 2017

Overall statement: It is a very good course ! The videos are very nice, and Professor Ghrist gives a "cool" touch to this subject. But some exam questions do not refer to material treated in the video and some explainations are too fast. Several times on the discussion forum, it is referred to the Penn Calc Wiki, whis is not in the references so a bit hard to follow ! But I definitely learned much, so i am very grateful for this, Thanks Professor Ghrist, Thanks Penn, Thanks Coursera :)

By SIngular S

â€¢Dec 17, 2019

I think it's a pre-calculus class, cause all the topic this class teaching are involved in calculus but not very deep, it's a broad content about calculus, I feel like I have learnt something but don't exactly know what degree is truly understand these knowledge and how these are connected together.Guessing it is a fresher's must-be stage,And really appreciate teacher for your clearly explanation and fabulous problems.

By Stephanie P

â€¢Apr 27, 2020

The course was really and challenging. This class goes deeper into the Taylor Series than most Calc II classes and I have a much better understanding of the material. The only thing I would like to see is some of the problems, especially the challenge problems worked out,. Maybe supplied at the end of the course? The last section on Big O gave me some trouble and I would have loved more detailed explanations.

By YaÅŸar E D

â€¢Aug 31, 2024

That was a great course overall. Some topics were challenging because the videos didn't go into as much depth, so I had to do additional research to tackle the tougher problems. It's perfect for brushing up on math after high school, especially if you're a freshman in university. I also recommend staying on top of the deadlines. Definitely worth taking. Thanks!

By aihui

â€¢Jan 6, 2018

The lecture provides a different view on calculus compared to the similar lecture during my university and this lecture is much better absolutely. I can still remember the suffering when i took my calculus course even though that was 5 years ago! I've got some confidence back in math and thanks for this lecture.

By Igor T

â€¢Jul 16, 2017

1) For me, the pace was a bit too fast. Gladly, there is an option to postpone the deadlines.

2) Graphical representations helped a lot in understanding the topics.

3) As for the challenge homework, I didn't feel like there was enough material in the lectures to do those tasks.

By Dmitry P

â€¢Oct 7, 2018

That's is really hard course. I think lecturer gives not enough information for doing homework. For example: big-O notation confuse me and I learn a lot of materials from another universities from web. Single web page for help that recommented in course is broken.

By Fu-Cheng C

â€¢Aug 28, 2020

The course is fun and provides a different but enlightening perspective on calculus. The only negative aspect of the course would be that certain course mentors were not that friendly and may even be condescending. This discouraged me from asking questions.

By Todor B

â€¢Jun 19, 2016

The class is OK but keep in mind that your algebra should be refreshed before starting it. I did not refresh my pre calculus knowledge and I had hard time solving some if the task just because some straightforward simplification were long gone form my mind.

By KhÃ¡nh L T T

â€¢Aug 2, 2022

I wish there were solutions for those exercises and challenges, some are very tough to me and I can't understand even after reading all discussions in forum...However, thanks a lot for lessons in this course, this partly help me in learning Calculus!

By Khang N

â€¢Jun 28, 2021

The course is well design and informative. However, there should be a list of recomended textbooks. The text included in this course is a site which is unreable due to the format. All the formulas and examples are out of fornt and cannot be read.

By Javier V L d M

â€¢Nov 4, 2017

El curso fue muy interesante, la metodologÃa fue clara y las explicaciones por parte del profesor fueron muy organizadas y coherentes. Pienso que en la funciÃ³n O grande hizo falta profunidzar y ejemplificar un poco mÃ¡s. Felicitaciones

By Sai M

â€¢Jan 7, 2021

Loved the course!!! Very interesting and a good refresher for learned concepts.

One suggestion: to explain week 1 with more examples especially functions. I felt the video lecture dropped me down a cliff while attending its quiz.

By Junaise

â€¢Apr 24, 2016

Very nice classes and concept. The presentation was excellent. But the lectures are too short and to the point only and dosnt elaborated with variety of examples. The demonstrations with graph and Multimedia is excellent.

By Sonia C

â€¢Apr 11, 2021

content is amazing and the practice questions are very challenging. Many thanks to professor Ghrist for the high quality, but it would be nice to add videos solving some of the harder questions in the homework session.