Back to Calculus: Single Variable Part 1 - Functions

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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....

DP

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Very creative way of teaching one of the most important and difficult applied math topic. The course is taught differently then traditional textbook and is challenging as well.

YX

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Very good refresh course for calculus. Content could be tough and require a lot of thinking. But I learned a lot or reviewed a lot about the calculus concept in my college year.

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By SIngular S

•Dec 17, 2019

I think it's a pre-calculus class, cause all the topic this class teaching are involved in calculus but not very deep, it's a broad content about calculus, I feel like I have learnt something but don't exactly know what degree is truly understand these knowledge and how these are connected together.Guessing it is a fresher's must-be stage,And really appreciate teacher for your clearly explanation and fabulous problems.

By Stephanie P

•Apr 27, 2020

The course was really and challenging. This class goes deeper into the Taylor Series than most Calc II classes and I have a much better understanding of the material. The only thing I would like to see is some of the problems, especially the challenge problems worked out,. Maybe supplied at the end of the course? The last section on Big O gave me some trouble and I would have loved more detailed explanations.

By aihui

•Jan 6, 2018

The lecture provides a different view on calculus compared to the similar lecture during my university and this lecture is much better absolutely. I can still remember the suffering when i took my calculus course even though that was 5 years ago! I've got some confidence back in math and thanks for this lecture.

By Igor T

•Jul 16, 2017

1) For me, the pace was a bit too fast. Gladly, there is an option to postpone the deadlines.

2) Graphical representations helped a lot in understanding the topics.

3) As for the challenge homework, I didn't feel like there was enough material in the lectures to do those tasks.

By Dmitry P

•Oct 7, 2018

That's is really hard course. I think lecturer gives not enough information for doing homework. For example: big-O notation confuse me and I learn a lot of materials from another universities from web. Single web page for help that recommented in course is broken.

By Fu-Cheng C

•Aug 28, 2020

The course is fun and provides a different but enlightening perspective on calculus. The only negative aspect of the course would be that certain course mentors were not that friendly and may even be condescending. This discouraged me from asking questions.

By Todor B

•Jun 19, 2016

The class is OK but keep in mind that your algebra should be refreshed before starting it. I did not refresh my pre calculus knowledge and I had hard time solving some if the task just because some straightforward simplification were long gone form my mind.

By Khánh L T T

•Aug 2, 2022

I wish there were solutions for those exercises and challenges, some are very tough to me and I can't understand even after reading all discussions in forum...However, thanks a lot for lessons in this course, this partly help me in learning Calculus!

By Khang N

•Jun 28, 2021

The course is well design and informative. However, there should be a list of recomended textbooks. The text included in this course is a site which is unreable due to the format. All the formulas and examples are out of fornt and cannot be read.

By Javier V L d M

•Nov 4, 2017

El curso fue muy interesante, la metodología fue clara y las explicaciones por parte del profesor fueron muy organizadas y coherentes. Pienso que en la función O grande hizo falta profunidzar y ejemplificar un poco más. Felicitaciones

By Sai M

•Jan 7, 2021

Loved the course!!! Very interesting and a good refresher for learned concepts.

One suggestion: to explain week 1 with more examples especially functions. I felt the video lecture dropped me down a cliff while attending its quiz.

By Junaise

•Apr 24, 2016

Very nice classes and concept. The presentation was excellent. But the lectures are too short and to the point only and dosnt elaborated with variety of examples. The demonstrations with graph and Multimedia is excellent.

By Sonia C

•Apr 11, 2021

content is amazing and the practice questions are very challenging. Many thanks to professor Ghrist for the high quality, but it would be nice to add videos solving some of the harder questions in the homework session.

By Vashurin R

•Apr 25, 2016

Course is really cool, but oriented mostly on practical exercises and providing definitions. It would be much better if it had more formal proofs. Otherwise excellent course with a lot of challenging problems to solve.

By Daniel

•Jul 26, 2020

It is a really good course, with a lot of definitions used at undergraduate level and well explained. Nevertheless, I could not understand too much about Big O. Probably, more examples would be useful to clarify it.

By Nisarg K

•Feb 23, 2016

Would have preferred accompanying solutions. Just getting the answer ain't enough. Making sure my approach is correct is essential as well considering the course touches upon the absolute basics.

By Yusuf F

•Sep 20, 2020

There were certain advanced concepts that could have had a better and clearer explanation such as the “big O”. But on the whole it was a very good course and very much recommendable.

By a l s

•Jul 14, 2017

The course is intriguing. More practice questions and explanations will be good. And it will be beneficial if it can provide extra background knowledge (or link) for further study.

By Aditya T

•Aug 14, 2020

Very insightful. However, I believe (although I may be wrong) that certain methods and techniques required to solve the homework problems weren't explained in the course material.

By Oscar K

•Jul 25, 2021

Really enjoyable and well thought out explanations, but many examples went unexplained which I consider a waste since it would be useful to see the thought process of a solution.

By Francisco A

•Jun 7, 2020

I quite enjoyed the course, although I found it unnecessarily tough sometimes. I believe extra solved examples for convergence, geometric and binomial series could help a lot!

By Mount

•Sep 4, 2016

ppt真心做得很漂亮，但是这门课程不是一门入门课，面向对象是在已经掌握了微积分的前提下、希望对微积分进一步了解和巩固的学生，自然，有些地方的讲述是非常仓促的。

思路上讲主线一直围绕泰勒级数展开，也总是以泰勒级数为思考角度（包括后面part 2也是如此），个人并不是十分适应这种纯数学的方式，更喜欢感官上、性质上来把握，所以……仁者见仁智者见智吧 ^_^

By Krishna P R

•Jun 20, 2018

I have taken a calculus course at university which dealt with the epsilon-delta definition of things. Enjoyed the different approach as well, keep up the good work!

By Benjamin C

•Mar 19, 2018

Challenging, because begins with the infinite series, which are not a simple concept. Once complete, a much higher level of mathematical understanding is achieved.

By Ohedul I

•Sep 27, 2022

Its a very nice course for calculus, serise and function. Videos could be more descriptive with examples. Homeworks are nicely designed to cover the whole topic.