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

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.

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.

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!

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.

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

HARD!!!

Hard

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.

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.

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

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.

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.

Although still confused with differential equation, I have made great pregross on calculus, and even mathmatics. This is another to watch the world and reconstruct my mind facing problems.

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 !

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

Looking forward to Multi Variable Calculus.

It was very helpful to understand calculus and application.

this Vedio lesson and animation very helpfull.

Excellent set of courses! I really hope there will be a multivariable course in the same fashion.

Great course, although quite challenging at parts. Nevertheless, the fruits are rewarding!

This fifth unit is highly original! I loved the "digital calculus" part.

An introduction to numerical analysis was exactly what I need.

A course from the future of education!

I would highly suggest trying it out!

professor's explanation is the best.

So helpful and makes math beautiful