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Learner Reviews & Feedback for Calculus: Single Variable Part 4 - Applications by University of Pennsylvania

263 ratings

About the Course

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 fourth part--part four of five--we cover computing areas and volumes, other geometric applications, physical applications, and averages and mass. We also introduce probability....

Top reviews


Apr 5, 2020

The course material are very well prepared. The focus is on direct application in engineering field. The concepts have been presented very elegantly - it shows deep knowledge of Prof Ghrist.


Mar 9, 2020

Simply awesome!

I would love to learn the digital calculus and the multi-variate calculus online with professor Ghrist.

Thank you! Dr. Ghrist

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1 - 25 of 52 Reviews for Calculus: Single Variable Part 4 - Applications

By 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.


Jul 6, 2018

The course taught me about how calculus is used to explain probability and statistics. This is exactly what I need to began studying these areas.

By Rafael C

Jun 17, 2019

I can fully comprehend the purpose of this part, application, but the contradiction is that for students majoring in business, sociology or whatever, we're not bothered about how calculus can be applied in physics or geometry. Only the last part of probability is of interest to me. So I would propose that this part should be redesigned for different fields of application instead of integrating all different disciplines into one part, cuz much of the whole offering will have no connection with my later study. Yet the content of the course itself is good.

By Alex G

Jun 23, 2016

this was simply an amazing course, perfect for my skill level and exactly what i needed to learn. Thank you for the opportunity.

By Louis J C J

Feb 14, 2019

There is lots of material covered but the course hangs together well.

By Michael C

May 2, 2019

Great course.

By Kamran S

Mar 9, 2021

An amazing excellent course if you want a mini review of your engineering math. It covers most of the Calculus 1 and some Calculus 2, some differential equations and some basic applications that are basis for statics and fluid mechanics, statistics, and finance. Beyond that I loved the fun it had with math and how cool it goes above and beyond. A few drawback were 1.Forums were not active. 2. Course needs some maintenance work 3. sometimes questions are ahead or above what was thought. and finally it is not an easy introductory course and is mainly for reviewing and relearning. Before I forget: It gave a good touch on how to use the online math tools like wolframalpha. Thank you so much, "Prof. Ghrist"

By Paul K M

Sep 6, 2019

This was a tough course. The lectures are very good, but I did have to rely on a lot of other material to really make sense of the concepts. Nonetheless, this course has given me a structure to organize my studies. The homework is tricky but rewarding. I have a much better grasp of calculus than a few months ago. I could recomend this course to anyone who really wants to understand calculus and its applications.

By Behzad K N

Jul 9, 2020

I have been exposed to so many applications in this course, have been constantly challenged which I have enjoyed even though I feel my head hearts!

I am retired teacher so i am motivated by how Prof/g skillfully conveys his thoughts to a learner such as me. I am grateful:

By Gian M D G

Feb 3, 2017

Entertaining and well thought, it seamlessly concatenates many calculus ideas into one tight program. The treatment of the infinitesimal elements as being the focus of understanding every concept was brilliant. Professor Ghrist is indeed a fantastic tutor and guide.

By Jose D

Jan 28, 2017

This is a very educational MOOC. It summarizes major topics very efficiently while making the presentation agile and interesting. It includes a number of really good and challenging quizzes and homeworks.

I really like it so far!!.

By Mukund M

Oct 16, 2021

I am neither a student nor a teacher. I am retired engineer age 73. I had a very little chance to use my

knowledge in my carrier . I just joined the course for refreshing my past study.

I enjoyed the course very much. Thank you .


Jan 19, 2021

It's a really great Calculus Course with Fantastic-looking PowerPoints & Explanation. However, I hope there can be some Fundamental Questions included in the Practice Quizzes as to guide me through it :)

By Vishu B

Apr 6, 2020

The course material are very well prepared. The focus is on direct application in engineering field. The concepts have been presented very elegantly - it shows deep knowledge of Prof Ghrist.

By Aldo T

Jan 18, 2023

The Course is amazing and the teacher is He is a genius and has a great ability to transmit and teach difficult concepts even more so with his own library and multimedia

By Guillermo A

Dec 20, 2020

In the best style of professor Grist. Hard work, at times frustrating, but well worth it. Professor Grist makes this pain fun.

Thanks for the experience.

By Herve Y

Mar 10, 2020

Simply awesome!

I would love to learn the digital calculus and the multi-variate calculus online with professor Ghrist.

Thank you! Dr. Ghrist


Sep 2, 2021

This is amazing! I learnt a lot of knowledge, and this is crucial to my later-on academic processes. Thank you Prof/g!

By Sachin M V

Dec 10, 2016

Really its hard to complete as many questions are tricky, but now i feel very nice after completion.

By Rafer

Sep 15, 2019

the reading‘s math symbol is little complex for me.And it’s a good experience for me.Thanks Prof G.

By Ricardo S L

Apr 29, 2018

Great that prof does not feed you with a spoon, but makes you work to understand the content.

By Radoslaw J

Mar 17, 2017

The best math course I've ever seen, and also the best MOOC. The presentation is stellar.

By Ad v d W

Jan 17, 2023

Difficult, but doable. I liked the series so far but it's a lot of work and not easy.

By Juan C

Jun 21, 2021

Phenomenal teacher. I wish he would offer more courses (I took Parts 3,4 and 5)

By 杨佳熙

Jun 21, 2016

the first four session is free which is econmic friendly. show u my respect :)