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.

A bit difficult, but not truly when a good effort is made. No doubt interesting. Even a post graduate student will truly benefit from this course.

So far the most difficult chapter of the 5-part calculus course. This makes successfully finishing the course feel like a great achievement. Prof. Ghrist does a wonderful job explaining the concepts of this chapter. The structure of the course is also well-organized to gradually give the learner a better understanding of integration concepts and techniques.

The Bonus lectures are just great! I majored in Mathematics in university, and they're even enlightening to me. BTW, thanks for the introduction to Wolfram Alpha. It's really fun.

It is not an ordinary course in integration rather than a course that should be taught in universities! Wonderful ideas by Prof. Ghrist.

UN CURSO EXCELENTE, CON METODOLOGIAS ACORDES A LA ACTUALIDAD Y APLICACIONES AFINES.

Un consulta. ¿Cómo accedo al Certificado? Gracias

Enjoyed working through the Calculus course. Doing it on line is a bit of a challenge and takes getting used to the logistics of managing the lectures, making notes, working on the problems etc.

It would be very helpful if there was a text book or if we could easily print out the class notes. Currently, I go through the laborious process of making a pdf of the lecture, but that does not capture the whiteboard notes, so I have to physically go through the file, and create gaps in there so I can review the course and physically write in the whiteboard notes. I find the Penn Calc Wiki lectures to be excellent, but there is no way to copy that. I would be happy to pay for the PennCalc wiki lecture notes so the I would have it in my file for future reference.

Excelente, felicitaciones , solo que es triste no poder disfrutar al 100% un curso de esta calidad al no estar traducido al español, le agradecería que por favor lo traduzca del ingles al idioma español ya que solo esta parcialmente traducido.

nuevamente felicitaciones por la gran didáctica con la que imparte el curso y sobre todo por la calidad con la que enseña.

Week 1 was a tough material for me, but I now understand how to linearize the differential equation and find stable and unstable equilibria and what this means. Exploring discussion forums was pretty helpful. If you're taking this course and struggling, ask to instructors or peers in discussion forums- they're willing to help you!

As usual, Prof. Grist courses are outstanding.

I found this one a bit more difficult for comfort. A few times I felt like having hit a brick wall and couldn't go forward. I had to review the sessions multiple times. However, it was sure worth the suffering.

Looking for for the next one.

Very good course. I found the last week difficult - much more so than the previous weeks or modules, but overall, I learned a lot and am looking forward to Part 4 next!

Thanks Prof G for your novel take on the subject and for taking the time to share and teach us!

It was a challenging course that worked at the end. I suggest some mid section add-ons and supporting materials. The supporting text (Penn math link) was not readable. Suggest some kind of solutions to similar problems on the side as guide.

All these five courses are very hard and at the same time very thorough and informative. And it is very, very difficult to successfully pass their exams. Especially this third pad that was related to integral Thank in advance ، professor

it was very fanstastic to join and complete this course, the trainer was very talented, he explaned all the contant in a very easy way. If possible, please provide the certificate for the same. Thanks to the entire team.

This is an excellent course, giving a super, in-depth, coverage of Integration. I love Professor Ghrist's presentation and the visuals are the best I have seen. Really good challenging exercises as well. Thanks.

The way this course is taught is different from any classical way of teaching calculus. The course here is presenting the whole philosophy of calculus based on Taylor's series and this is really amazing.

I like it because it though me differential equations. This topics was previously missing from my education. It can be daunting to learn DE without proper guidance. This course provided just that.

The examples and the problems chosen are very thought provoking - the knowledge gained is fully tested by solving these problems.

I having been previewing Calculus over the summer and have taken courses from different sources.THIS COURSE DOES HELPS THE MOST.

Fantastic course. Buy his book.(kindle version is cheaper)

Checkout his website also.

https://www2.math.upenn.edu/~ghrist/