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....

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 !

SC

Apr 9, 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.

筛选依据：

创建者 Xiao L

•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!

创建者 Sanchit S

•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.

创建者 Nathan H

•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.

创建者 Subhayan C

•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.

创建者 Bartholomew G

•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.

创建者 mistique

•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.

创建者 Rohit B

•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.

创建者 Khadija H

•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.

创建者 MOHAMMAD Z

•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?!!!

创建者 Mary-Ellen W

•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.

创建者 Charles L J

•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.

创建者 Farhan N

•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!!

创建者 Mohammed A

•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!

创建者 Anna S

•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.

创建者 Sattvik G

•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.

创建者 Yang X

•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

创建者 Paul C

•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 !

创建者 Robert H

•Feb 3, 2017

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

创建者 Rafael C

•Jul 21, 2019

HARD!!!

创建者 Zhenan L

•Jul 30, 2019

Hard

创建者 Greg

•May 25, 2020

It's an amazing course. Prof/G developed a great approach to make complex things clear and simple. I was able to refine my calculus skills and knowledge and look on some very important things from a different angle understanding them more deeply. Awesome work!

创建者 Stephen S

•Apr 15, 2022

Great course; over-streched my 81 year old abilities but I thoroughly enjoyed the challenges. It certainly kept me occupied this winter. Thanks to Prof. G and all your assistants. (The test man was particulaly "devious," especially the final.

创建者 MELGAREJO E A

•Jan 1, 2021

I congratulate the work of Professor Robert W Ghrist. It tests our potential to pass. It was a pleasure to complete it successfully. It's a great course.

Note: the videos are very creative, it is a "bonus to consider"

创建者 Weinan H

•Aug 24, 2017

The course content is really satisfying. The difficulty in Challenges is quite cool while the homework problems and the tests are reasonable. I kind of of fell in love with math with Prof. Ghrist help.

创建者 Maximilian N J W M

•Jan 11, 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.