Back to Calculus: Single Variable Part 1 - Functions

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1,663 ratings

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452 reviews

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 2, 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.

NL

Feb 9, 2021

Excellent introduction to Calculus, I wanted to review the material to tutor my child but I am very happy that I learned a whole new way of looking at Calculus.\n\nThank you so much Prof. Ghrist.

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By Gabe E

•Jan 31, 2016

As I already have my Mathematics Minor, I wanted a quick refresher course. I would say this course is severely lacking in both practice problems as well as example problems done during video sessions. Students need more applied concepts to be able to understand and succeed if this content is not familiar. I got by only by preexisting knowledge of these Math concepts.

By Deleted A

•Jun 23, 2018

This course, which teaches calculus, assumes that the audience already knows calculus. That's so ridiculous!

By Benjamin S

•Apr 8, 2019

Amazing course! I took Calc 1 and 2 way back when and plan to attend college again starting this summer to earn another degree. Being Engineering, I wanted to brush up on my calc 1 and 2 before I dive into DiffEQs and Linear Algebera and this course did just that for me. The best part about it was that he assumes you alerady have a basic understanding of the material so its not like starting from square 1.

By Pooja R

•Mar 2, 2016

Not worth it - better to just read a book on calculus, as the homework questions at the end of each session does not even reflect one single example in the 16min session. Disappointed, but then again what can you learn in 15 min sessions, very little.

By Ynocencio G

•Jul 2, 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.

By Ryan H

•Dec 15, 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.

By Sg C

•Apr 7, 2019

Interesting starting point for calculus which makes intuitive sense. The visuals in the lectures are excellent, specifically on the explanation of limits. Taking this course is akin to reading a spy thriller book, the farther one goes the more intriguing it gets.

By Nayaka S R

•Jul 11, 2018

It was a great journey with Calculus with the help of Coursera. i learned many things about Functions, Taylor series and Order of Growth. Thank you for creating such a great platfarm for us.

By RAGAVAN N

•Jan 11, 2020

After being in the computer software industry for 12 years, I wanted to challenge myself with another full-time master's degree heavy on Math. It's been over 12 years since I set aside time any time to learn mathematics (I am 35 years old now). Now driven by the need to refresh my basic math skills I enrolled in this course.

Prof. Ghrist is a very passionate teacher who has not only clearly made significant efforts to create this material, but delivers it in a structure and style which will help you build rock solid foundation of single variable calculus, IF you work on all the homework assignments. He divides the homework into "core homework" and "challenge homework", and I feel that doing all of them is essential to gain mastery of the material. The problems in the homework are non-trivial and make you think.

For those interested, Prof. Ghrist has also published Kindle-only ebook (several volumes, east costing less than a Starbucks coffee) on Multivariable Calculus where he walks through the concepts in the same style, covering all the basics. I have already purchased volume 1 of it, and I am excited to work on the problems in the remaining parts of this course, and then read his ebook on Multivariate calculus.

I feel very thankful to Prof. Ghrist for this wonderful work, and to Coursera for bringing such advanced material from exceptional teachers for people all across the world.

By 江祖榮

•Jul 14, 2019

Great one.

Teacher Ghrist is good at providing thought-provoking insight and visualization of basic function, math formula as well as series expansion.

In addition, this course starts with a set of basic functions and domain knowledge such as simple polynomial, trigonometric, exponential, natural log, hyperbolic trigonometric, simple derivative and integral, and so on.

Then we will go through Taylor series and its expansion. To be honest, Taylor series as well as expansion is the key essential part of this course, it is not only useful for us to evaluate function value and its error of a given point, but also practical to get better understanding of limitation within 0/0 and ∞/∞ as well as L'Hospital's Rule later.

Finally, this course ends with analysis of function growth rate, upper bound of function when it comes to zero point or infinity, and the application of L'Hospital's Rule.

It is strongly recommended taking this course to start our wonderful calculus journey.

By Matthew A

•Oct 15, 2017

Great introduction to calculus/analysis. Covers a good range of functions and applications. Starting with Taylor series is an approach I hadn't seen much before, it worked well. Fantastic graphics and animation, they make for a rather cool pedagogical aid. Prof Grist's delivery is another plus, it's simply very good.

My only concern is in treatment of 'Big-O' notation, I feel that the link with limits is not spelled out and expanded upon as well as it might be. Then again, I may not have understood things correctly.

Anyway, overall a very good course. Highly recommended.

By Stefan F

•Jun 30, 2019

Interesting approach to start a calculus lesson. I liked it very much although I can understand that some people dislike the steep learning curve. On the other hand it was stated from the beginning that this is a tough course. Summarized I learned a trick or two for which I am grateful. Thanks! Lastly there are active mentors in this course that are very helpful. Overall the course is very recommendable for advanced and curious calculus students.

By Anthony D

•Jan 31, 2019

Excellent course from a great school and excellent professor. The videos were informative. I found this class to be very challenging. I ended up with an A and look forward to the next parts. I think you need some exposure to calculus before taking this class. I took calculus 8 years ago.

By Nikita S

•Apr 30, 2018

Unexpectedly interesting course on Calculus, some of the extra problems are really difficult. With a total of 109 problems and many colorful lectures, it is one of the best courses on Calculus in English. - Nikita Skybytskyi, winner of the International Mathematical Olympiad

By John H

•Feb 11, 2018

Good course but lecture material was not quite comprehensive enough to tackle the questions with confidence.

By Ruhollah E

•Jan 29, 2018

very difficult for first time learner

By Brittany B

•Feb 1, 2016

What a great course! I can tell that a lot of thought and effort went into the structure and material of this course. Firstly, I liked how the first week started off with just the diagnostic test which exposed some weak areas and gave me the time I needed to review some topics that I had forgotten (like inverse trig). Secondly the lectures themselves were clear and easily digestible with lots of cool visuals to facilitate memory and understanding . Thirdly, I'm already seeing the pay-off for learning about the Taylor series first, especially when it comes to evaluating limits. Lastly, I actually had fun learning calculus which for me is a big deal since I usually have to struggle terribly to learn anything math-related. I'm looking forward to the next section.

By Xiao L

•Nov 14, 2017

This course is marvelous! I actually majored in Mathematics in university. But our Calculus course (it was called Mathematical Analysis, BTW) focused on every detail of the δ-ε proof of every theorem and formula, and I didn't get a chance to see the big picture. Now that this course is enlightening to me, I believe it would be useful for the majority. I think I'll take the whole series of five courses. Anybody know when the multiple variable series is coming?

A slight digression, though. Professor Ghrist talks a bit like Chandler Bing. With all the respect, it was funny sometimes. Fans of FRIENDS should understand what I'm talking about.

By Matthieu B

•Aug 18, 2019

I loved this course and its style ! There's a lot of colours and animations so it makes the course funny and attractive (more fun and attractive than classical math courses in high school and in many universities). Thank to professor Ghrist, I've finally understood the utility of Taylor series, the real meaning of a limit and other things. I'm going to follow the next chapters and I'm waiting for another mooc about multivariate fonctions : I hope professor Ghrist didn't forget it and that it will be quickly available. :D

By Taeho K

•Nov 5, 2018

This course is a good for refresher for people who took A-Level Further Mathematics or equivalent. By taking the course, you'll be able to look at functions in a different way. The questions are also slightly time consuming (or should I say 'challenging') which helps you have a solid understanding.

By K.S.S.UDUPA

•Jan 26, 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 Derek S

•Jul 21, 2019

Enjoyed the whole journey in this course. Beautiful graphics, choir-base-like sound, concise explanation and instrumental exercises. Thanks Prof. Ghrist.

By Joseph S L

•Jul 9, 2019

Ghrist makes math fun by putting a twist on the lessons. It may look childish/cartoonish, but Ghrist obviously understands what younger people well.

By Nikita V

•Jul 24, 2019

Great course! Material is really dense and highly practical. Thanks!

By Ng T E

•Nov 13, 2020

Very challenging course, even for a Calculus enthusiast like me

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