Back to Calculus: Single Variable Part 1 - Functions

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2,143 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....

JV

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Very Informative course and easy to catch. Although knowledge on the subject is a prerequisite before taking this. Not advisable to those with no knowledge whatsoever in calculus.

AT

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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.

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By Ramajeyam K

•Jul 15, 2017

Great

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•Apr 5, 2024

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•Nov 5, 2023

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•Nov 5, 2023

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•Feb 13, 2023

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•Feb 5, 2023

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By Mr.Raman C

•Jun 11, 2022

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By Chandrashekhar A B

•Apr 20, 2022

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•Dec 7, 2020

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By Kunal V

•Mar 5, 2020

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By 李松涛

•Mar 23, 2019

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By 顾雪

•Mar 30, 2017

good

By 星 田

•Jan 24, 2016

很好

By Erkin B A

•Apr 7, 2024

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•Oct 7, 2023

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By Joao M d C

•Jun 9, 2021

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By 洪啸宇

•Jun 19, 2016

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By Helena R

•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

•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

•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

•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

•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

•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

•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

•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 :)