Calculus: Single Variable Part 1 - Functions に戻る

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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 first part--part one of five--you will extend your understanding of Taylor series, review limits, learn the *why* behind l'Hopital's rule, and, most importantly, learn a new language for describing growth and decay of functions: the BIG O....

Jul 03, 2018

Very well structured for a refresher course. Thank you Professor Ghrist for your effort in putting this course together. A little additional outside research was required but well worth the effort.

Dec 16, 2016

Excellent class. Prof. Ghrist has a great teaching style, and his idea to use Taylor Series first is quite effective. Many functions I have shied away from in the past are now familiar to me.

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by Pedro R

•Dec 26, 2018

It's a very good course that uses a different point of view to understand how things works in calculus. It's very didatic and helps you think outside the box. If you're thinking about do the course, keep in mind that it is necessary previous knowledge in calculus.

by ZIXIANG Y

•Jun 17, 2018

I would highly recommend this course to those who are trying hard to study calculus in Chinese universities but having a hard time understanding calculus. After finishing this course, you will find it useful to use Taylor Expansion to solve limit problems in tests.

by Dmitry P

•Feb 14, 2018

For me the most difficult part was "order of growth". It would be very nice if this subject was explained more detailed. It was rather hard course for me (I can't do all the exercises in time). Big thanks for many exercises and for few errors.

by Tracy S B

•Feb 02, 2020

Excellent course. Thanks!

Future Students: Make sure you read the Wiki in the "General Discussion" section titled "READ ME!!!!!!!!!! Penn Calc Wiki supplement" because that will tell you where to find the web-based "textbook" for the course

by Robert H

•Feb 25, 2016

The YouTube description was overly enthusiastic. The course description on signup was much more to the point: This is not AB calculus. Reach the end and you will have accomplished something. Warning: You will not be led by the hand.

by Rene G

•Mar 08, 2019

This course was intense for me, sometimes I had to view lessons more than once to get the point.

If you are not a pro but have the impression that you begin to master calculus then this course will be an eye opener, hard but doable.

by Marat K

•Aug 03, 2016

Colorful and quite clear, but it might be a bit impractical (and I've been out of school for years now) in my case, so I'm just reviewing it to recall some notions and theories - and just for fun and a bit of mind-crunching :)

by João D M P

•Jan 03, 2016

The taylor series insight on growth orders and differentiation as well as function definition is invaluable. The lecturer is superbly original in both presentation of the material, but also on an integrative exposition.

by trshant

•Mar 25, 2016

i am finally beginning to understand calculus!

It is perfectly paced, and the core homework, while simple really makes you think about what you learned. And prepares you for tougher things, like the challenge homework.

by Hayk M

•Sep 15, 2019

Overall, the course is very useful and well structured. I think in some parts of the videos, other methods of explanation should have been chosen in order to allow students to grasp the content of the course easily.

by I.W.

•Dec 28, 2018

This was great, thank you! The only thing that would be useful is solutions to missed problems after the assignment has been completed because it's hard to know what you did wrong when you are working by yourself.

by Utkarsh R

•Jan 09, 2016

Feeling calculus!

I'm loving this series of lectures. If you have taken any basic calculus course before, this is the perfect course.

I wish to thank Professor Ghrist and University of Pennsylvania for this course.

by Abdulla A

•May 26, 2019

Wonderful course delving into the basics of calculus. I loved the explanatikon and colors. Although I am still not sure about Orders of growth, everything else was explained perfectly and enthusiastically.

by Mengyun Z

•Jun 14, 2016

The lectures are delivered in a clear and straightforward manner. Videos do a good job in walking me through the key points related to the topic. And the exercises were well designed to capture the

by Stephen w

•Jun 02, 2018

This course is difficult, and sometimes is not easy to know how to correct the homework questions since there are no analysis of them and the answers in the forum are not quite complete.

by K.S.S.UDUPA

•Jan 27, 2016

This module is fully exhaustive. You will also understand why we need series expansion of a function at a given point and its convergence and other applications. I enjoyed it thoroughly.

by JHONNY L L

•May 14, 2019

I really liked this Calculus course, there were many interesting problems and with a good degree of difficulty. I give them five stars, and I greatly appreciate them for this course.

by Ning L

•Oct 28, 2016

What can I say? It is so good that I watch the lectures when I have dinner alone. Prof Ghrist absolutely has presented calculus so well that it becomes such an entertainment!

by Sagar G

•Nov 30, 2018

Great UI and explanation.Started with the Engg. maths and taking it to high school and for the Developer like me Big O is something which introduced in a appropriate way..:)

by Pietro R

•Jun 16, 2018

I easily understood concept that i never understood before. I'd say that this is the perfecto goal of any possible course: make understandable the not-easily-understandab

by Bongani P

•Jul 14, 2017

This is one of the best mathematics courses I have ever taken. The lectures are straight to the point and the homework's are very very challenging. Thoroughly enjoyed it.

by Daniel M

•Apr 15, 2016

I have already taken it once. I am taking it again now. A wonderful course. I am always amazed at how clear Prof. Ghrist's explanations are. Thanks for this course.

by Wolfe G

•Feb 17, 2017

A little scary to start with Taylor series, but once mastered, it gives a depth of understanding not given by other MOOCs I have found on the subject.

by Wenkai L

•Jan 08, 2016

This course is very great and helpful. However, I think the course should provide more exercises to help students comprehend the new knowledge better.