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....

YG

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.

KR

Aug 18, 2020

Very good and challenging material! This motivated me to do better in my Calculus Courses. Would definitely have more of these courses soon, as this is suited for higher mathematics in college.

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by Darleen J T S

•May 18, 2020

A very useful course to reinforce and measure your knowledge of simple variable calculus at the level of functions, limits and Taylor series. I especially thank the teacher R. Ghrist and his collaborators for the didactic material that they have given us as well as for the challenging problems that they have posed to solve.

by Patrick S H

•Oct 05, 2019

I really appreciate the work that Professor Ghrist and the online curriculum team have put into making classes like this so accessible. I didn't feel like I was up to my knees in spam-can explanations, and just left to my own devices. Professor Ghrist is actually a very good tour guide for some very interesting territory.

by Okto T

•Dec 20, 2019

Amazing course, taught by a brilliant professor. A very useful course for me, as my previous calculus experience did not include Taylor Series. The homework took me a lot of time though, always over an hour. I didn't always manage the challenge homework. Overall very satisfied and looking forward to the next part.

by Alperen Ç K

•Sep 05, 2020

Very well organized course with clear explanations. Plenty of visual slides which makes understanding better. Professor is also focusing on many details that normally requires proper explanation and he does explain those details clearly. The focus is on the Taylor Series. I can't wait to finish other parts!

by Shaurya A

•Jun 04, 2020

Course overall was great. The Professor Robert Greist explained wonderfully and the animation was also great. But there was a gap in the understanding about the big O and asymptotics specifically in week 4 lecture : Orders of growth

But everything else went in a great flow.

Looking forward to calculus 2

by Brian N A

•Jun 24, 2018

I enjoyed the course, and I will be taking the other parts of it too. The problems seem well designed to expose flaws in your thinking. I still feel somewhat shaky on some topics, but I would say the overall concepts came through very well, and the journey through them was cohesive and well laid-out.

by Akshath M

•Apr 30, 2020

I really loved it, to be honest. I am a high school student, and, I had some exposure to calc before, but, when I took this course, I got bombed on the first attempts lol. It was really tough and this has been my first ever course which really tests my brain. Honestly, I have learnt a lot of stuff.

by Mikayla B

•Jun 19, 2016

This course offers so much! I haven't been in a class that goes this in-depth in calculus. I definitely recommend this course to others who want to explore calculus and want a challenge!

Best of luck to those who choose to enroll in all 5 parts of single variable calculus sessions. It's worth it :)

by Carlos A

•May 03, 2017

It was great, the lectures were amazingly done, I loved all the colors and stuff made.

Clear and understandable.

Exercises not too hard, not too easy.

Our starting point is Euler's identity and Taylor Series, wich we take as a given. I didn't like it very much, but, overall, it accomplishes its goal.

by Don H

•Mar 02, 2019

It's not perfect, but no course is. This course won't raise your test scores (at least not immediately). To do that, you have to buckle down and study the material assigned by your professor. But if you want a deeper understanding of the concept, I couldn't recommend a better course or platform.

by michael f

•May 18, 2017

I thoroughly enjoyed this course. Prof. Ghrist is an excellent teacher. The course was a tad bit harder than i has expected it to be, but nonetheless, i thoroughly enjoyed it and would recommend it to anyone who has an interest in Mathematics and calculus. It also cleared some of my concepts.

by Valerie C

•Mar 07, 2016

I found this course to be very helpful, challenging, informative, and well-made. There was obvious a lot of time and effort put into making the videos. I have a good amount of math experience, but I still found it challenging and interesting. I'm very happy to have found this resource.

by Kannadasan P S

•Jul 15, 2020

Got to know to some of the crucial concepts like Big-O which was a base for complex computation in the calculation of time for programmes. And the lectures were very interesting as they were explained with application. The overall feel while learning the course was good !!

by Aleksey C

•Dec 29, 2016

When I retake homework tasks I try to fix tasks I failed on previous attempt. IMHO it make sense to not repeat them all but provide only tasks that were solved incorrectly. Repeating ALL tasks just wastes my time for reentering correct answers and is error-prone process.

by Ross L

•Nov 27, 2018

This is a much more in-depth calc class than I've had at univ, and by more in-depth I mean it's harder. That being said I feel like I understand the material better as before there was much more memorization whereas this has more explanation. A++++++ would take again.

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 Eskinder T

•Aug 12, 2020

Challenging but worth the time and effort. One could memorize formulas and solve calculus problems. In contrast, this course helps to understand the underlying reasons and links different topics in calculus. Thank you Professor Ghrist!

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

•Jun 23, 2020

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.

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