Back to Single Variable Calculus

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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 fifth part--part five of five--we cover a calculus for sequences, numerical methods, series and convergence tests, power and Taylor series, and conclude the course with a final exam. Learners in this course can earn a certificate in the series by signing up for Coursera's verified certificate program and passing the series' final exam....

MM

Jan 10, 2016

This course is tricky and also excellent. I am a computer science student from germany, and it took me quite some time and effort to pass it. The course is well structured, and can be done in time.

PC

Sep 14, 2019

Loved it ! I've grown attached to Prof. Ghrist's lectures, so it is with a heavy heart that I took the final exam and finished this course. I xould really love to take another !

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By Xiao L

â€¢Dec 4, 2017

Again and again and again ... love the bonus lectures! Really enlightening! Please release the Multi-variable Calculus ASAP! Can't wait to take it!

By Sanchit S

â€¢Aug 21, 2016

Hey guys. So I just completed a Discrete Calculus course, offered by UPenn, through Coursera. I'd like to give a you guys an overview of the course, and my experience through this journey.

This, 5 part course, is designed to be completed within 21 weeks, with a work time of 6-8 hours a week. However, if you're really dedicated and have enough time, you can probably finish it within 8 weeks (like me). Oh, and it is taught by Prof. Robert Ghrist (he's cool, trust me).

First, for the prerequisites, you should have taken at least Calculus AB, to do well in this course. Practice with advanced integration techniques and some prior knowledge of Taylor Series is a plus.

Part 1 of the course begins with a study of Taylor Series. From what I've noticed, part 1 emphasizes the importance of using Taylor Series to develop an intuition about the behavior of a function at limits such as 0 and infinity. After revisiting some familiar topics with the perspective of Taylor, part 1 ends with introducing asymptotic analysis (big O), which took me a while to grasp.

Part 2 is review for the most part. However, it helps to further strengthen the idea of differentials, and their uses. Some bonus lectures introduce topology, and spacial curvature. Also, there is an introduction to the algebra of operators (which is elaborated in part 5) Some BC topics are also reviewed.

Part 3 mostly deals with practicing integration techniques, however emphasizes on Differential Equations (with specific focus on coupled oscillators). Formal definite integrals are introduced. Some more BC topics are reviewed.

Part 4, focuses on applying knowledge from the preceding parts. Although it starts off easy with areas, volumes, and arc length, the focus shifts to statistics and physical applications. There is a weird study of Work. Rotational Inertia and PDFs are taught in tandem. There is a brief study of high dimension spaces and hyper volumes. Centroids are taught through the use of double integrals.

Finally, part 5 introduces discrete calculus. Basically, continuous calculus, retaught with the perspective of series, in a discretized, non continuous setting. It begins with the study of finite differences, and a rather comprehensive practice of discrete integration. Differential equations (aka recursion relations) are taught, through the use of operators. Then, the focus shifts to numerical analysis, by introducing methods to approximate integrals (like Runge Kutta method). Following that, there is a very comprehensive study of convergence of series. And trust me, it is taught super well (way more in-depth than BC). Finally, the focus shifts to the rather obscure Taylor Remainder Theorem. This might be review for some.

This course was pretty challenging for me. I spent a lot of time doing my homework, and taking really good notes (for future reference). After a fee of $50, I earned my course certificate after the final exam (sigh).

This is a super cool course.

By Nathan H

â€¢Oct 12, 2018

There are assignments in this course that leave the student unprepared to pass based on the material. The discussion forums point to trying harder or using other methods, but offer little help. It looks as though students spend weeks on completing a single HW assignment. A simple format change would go a long way in testing the students' understanding while not just giving them the answer.

By Subhayan C

â€¢Apr 10, 2020

A fantastic course. Kudos to Prof. Ghrist for making this a fun, interesting and challenging ride at the same time. Looking forward to Multivariable Calculus by Prof. Ghrist.

By Rohit B

â€¢Feb 11, 2017

Feeling really great after finishing the course. Learnt a lot and gained deeper insights into the calculus.

Looking forward to Multi Variable Calculus.

By Bartholomew G

â€¢Feb 11, 2020

I cannot overemphasize how bad this course is. The instructor speaks in a bizarre, halting cadence that in no way tracks natural speech, and more closely resembles The Twilight Zone's introduction monologue as delivered by your eager-but-untalented uncle. Needing to listen to these lectures makes it nearly impossible to penetrate through to the material itself.

As to the material, the course begins with Taylor series without giving any explanation for how Taylor series work. I paid for the course upfront as a motivating tool but I dropped it and took another calculus course instead. It's that bad.

By MOHAMMAD Z

â€¢Jun 2, 2020

Absolutely horrible! The tone of the lecturer is mocking and silly! which makes concentrating on the material that is being taught almost impossible. Also choice of teaching style and explanations of various complex concepts is so poor that I needed to supplement this course with Khan Academy and other videos on You Tube, only to make sense of what the lecturer is going on about. I do not recommend this course to anyone in his/her right mind, specially for such a challenging topic in calculus. what a silly university lecturer, what is that tone?!!!

By mistique

â€¢Dec 30, 2019

This guy doesn't explain anything in terms I've learned during a calculus class. I've completed all of my calculus courses and just was hoping for a refresher, but this is one of the worst layouts I've seen. Also he sounds like a computer and the whole thing is just a shit show. Thanks for the MOOCs but this guy needs to change or go.

By Khadija H

â€¢Jan 30, 2019

Challenging but worth it! I did have to use supplemental tools to aid in my learning but that may not be the case for everyone.

By Mary-Ellen L

â€¢Dec 24, 2020

The course was challenging and interesting. The homework was mostly fine, but one core homework set was almost impossible to pass (Week 3 Convergence Tests II), and the responses from one of the TA's in the discussion were so insulting and unhelpful that I didn't dare ask for any help.

By Angela N

â€¢Aug 5, 2021

I've taken calculus classes online before and chose this class as a refresher for my upcoming Calc 3 study this year. First of all, this is NOT a good introductory course. It is the fifth part in a 5 part calculus sequence, and the final test, which is worth over half your grade, reflects on concepts that were not covered once during this course. Even the first few classes begin talking about Taylor Series, which I imagine would be extremely difficult for a beginner to understand.

I haven't taken the full sequence, so perhaps my experience would be better if I did so, but from the perspective of someone that saw this single class as an all-encompassing calc course, that was something I didn't like.

Prof. Ghrist isn't awful at explaining calculus, but I've learned from far, far better instructors (Sal Khan from Khan Academy), to name one. I enjoyed the exercises provided by the course, but I also strongly disliked that there was no given feedback or explanation from any homework answers.

Overall, not really a fan. And the TAs in the discussion forums weren't so helpful either.

By Charles L J

â€¢Feb 6, 2020

The videos are unwatchable. I have never heard a professor speak with that vocal fry faux-ASMR but it was completely unnecessary and distracting to the content being presented. I thought it was a joke voice but he kept doing it.

By Farhan N

â€¢Jul 5, 2020

I couldn't take calculus at university and this course offered me an opportunity to cover most of the topics in single variable calculus. Its tough, well taught, the staff is helpful and questions are great. The videos are very nice with animations and humor here and there, which really keeps things interesting. Supplement this course with a book on calculus (AP calc BC or stewart's calculus) to cover some topics like mean value theorem, polar and parametric coordinates (covered here but light) in more depth, and for getting some more practice on weak areas.

Loved it and will definitely be looking into the multivariable videos soon.

NOTE: the course assumes you have covered basic calculus upto AP calc AB. So make sure you cover that before you get into this one!!

By Mohammed A

â€¢Jun 26, 2018

This was a great course. It was my first time learning about single-variable calculus with Taylor Series at the heart of it. It gave me a deeper and better perspective. It was also my first time learning about topics like orders of growth and big-oh, forward differences, Fibonacci and Pell sequences, falling powers and discrete calculus. I had a blast learning about them. The professor also introduced ODEs, probability, discrete mathematics and numerical methods. He got me interested in taking a course on each one of these subjects. The design and execution of the video lectures was excellent. Homework and exam problems were challenging and helped solidify my understanding of the material. Don't miss this course!

By Anna S

â€¢Oct 16, 2017

An excellent course, very challenging, but doable and enjoyable. A lot of thanks to professor Ghrist and his team for the tremendous work on building this course and for my improved level of understanding Calculus. I have just started the university course of classical mechanics, and all problems incluling Calculus seem to be so easy after this tough training. Also a lot of thanks to all of the mentors, for their dedication, patience and and help. If the Multivariable Calculus course by this team becomes available, I definitely will be among its first students.

By Sattvik G

â€¢Feb 4, 2020

A complex and completely new course of Mathematics. It opened to me a world of single variable calculus that I had never thought much about before namely discrete calculus. Professor Ghrist is a really good teacher and so I would recommend this course to anybody who wants to learn a different aspect of calculus. This is also the only course of the 5 part series that gives a certificate upon completion.

By Yang X

â€¢Mar 6, 2016

This whole series is just amazing. It teaches Calculus in a way that's so different from how it is taught in most universities. I thought I would never be able to do Calculus but I was really successful after finishing the 5-course series in 2 months. Highly recommended

By Paul C

â€¢Sep 15, 2019

Loved it ! I've grown attached to Prof. Ghrist's lectures, so it is with a heavy heart that I took the final exam and finished this course. I xould really love to take another !

By Ohedul I

â€¢Dec 20, 2022

very well organized. One needs to really think deeply and in a critical way to solve some of the questions. recommended.

By Robert H

â€¢Feb 3, 2017

That was a brilliant journey through Single Variable Calculus-land. Well done Prof G and team! Thanks for the ride.

By Peter S

â€¢Oct 7, 2023

really helpful, great animation but I hope there can be more explanation or extra material to learn

By Shun D

â€¢Dec 31, 2022

It's very challenging. But with grit and determination you can pass.

By Rafael C

â€¢Jul 21, 2019

HARD!!!

By Zhenan L

â€¢Jul 30, 2019

Hard

By wangzuqiao

â€¢Dec 19, 2023

Lecture is fine, homework take a lot of time to finish, and some multiple answer question was stressful as you don't know how you got it wrong and need recalculate it again and again. Take much longer than the time is shown, and the final exam is kind of far away from this class ,especially only taking this one class without what told before in this course like me. Best regard for the unlimited attempt .