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Back to Calculus: Single Variable Part 3 - Integration

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464 ratings

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 third part--part three of five--we cover integrating differential equations, techniques of integration, the fundamental theorem of integral calculus, and difficult integrals....

CC

Jul 1, 2018

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.

XL

Nov 21, 2017

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.

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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 Omar J

â€¢Nov 10, 2018

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.

By Xiao L

â€¢Nov 22, 2017

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.

By WALTER S T

â€¢Sep 29, 2020

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

Un consulta. Â¿CÃ³mo accedo al Certificado? Gracias

By Ashley S

â€¢Nov 9, 2020

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.

By Gregorio A A P

â€¢Jul 8, 2017

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

nuevamente felicitaciones por la gran didÃ¡ctica con la que imparte el curso y sobre todo por la calidad con la que enseÃ±a.

By Hyorin N

â€¢Nov 9, 2021

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!

By Guillermo A

â€¢Apr 18, 2020

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.

By Kamran S

â€¢Feb 1, 2021

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.

By Rajni G

â€¢Aug 4, 2021

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.

By John H

â€¢Apr 14, 2020

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.

By Abd A A R E

â€¢Jul 6, 2020

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.

By CMC

â€¢Jul 2, 2018

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.

By Abhijit B

â€¢Jun 17, 2016

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.

By Vishu B

â€¢Feb 18, 2020

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

By Ann

â€¢Aug 17, 2016

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

By Infant J E

â€¢Aug 21, 2022

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

Checkout his website also.

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

By Oap T

â€¢Nov 25, 2020

A very good course for someone who is decent at mathematics and wants to study calculus AFTER HIGH SCHOOL CALCULUS.

By Jorge E M L V

â€¢May 31, 2019

Excelente curso de verdad que es muy bueno hacerlo ya que se aprende mucho del cÃ¡lculo integral en una variable

By æ±Ÿç¥–æ¦®

â€¢Aug 2, 2019

Great lecture of integration with a tons of practical thought-provoking example and illustration.

By gibanez78

â€¢May 7, 2022

Overall great Experience. Quite challenging though, but Professor Ghrist is simply the best.

By Oscar O

â€¢Sep 16, 2020

Thanks Dr. Ghrist......just a truly superb course.....not easy at all, but really great.

By Alassane K

â€¢Apr 26, 2017

I have really enjoyed learning materials from this course. This is a great chapter!

By Bhavik P

â€¢Dec 9, 2016

excellent course ..please guys enroll and learn with best prof...Robert Ghrist....

By Jorge P

â€¢Apr 26, 2018

Just superb, not easy, challenging but so well prepared. Thanks for it Dr Ghrist.

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