Back to Calculus: Single Variable Part 1 - Functions

4.8

1,024 ratings

•

264 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....

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 Benjamin S

•Apr 08, 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 Ynocencio G

•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.

By Ryan H

•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.

By Gabe E

•Feb 01, 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 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 Joseph S L

•Jul 09, 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 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 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 Nikita V

•Jul 24, 2019

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

By SG C

•Apr 07, 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 kathleensa

•Jul 23, 2019

wonderful experince

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 Mubashir-Ul-Hassan

•Aug 06, 2019

One of the great course which helps me to Revise and also fill the missing topics

By Kevin L

•Jun 23, 2018

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

By Pooja R

•Mar 02, 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 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 Zheng J Y

•Jan 29, 2019

It's a very nice course. I strongly recommend it no matter who your are, as long as you what to learn calculus.

By Robert H

•Nov 26, 2018

Great course! A particularly novel and extremely well-done presentation of the basics of calculus, part of a multi-course sequence that covers the whole of single variable calculus. Also worth a serious look is Professor Ghrist's material on multivariate calculus, available on You Tube. See his Penn web site for more details (http://www.math.upenn.edu/~ghrist/).

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 Misty K

•Nov 27, 2018

I appreciated the in depth theory and mechanics.

By augustin m k

•Nov 12, 2018

the course was good for me ,i undestand it very well

By Saptarshi C

•Jan 16, 2019

Excellent course. A little bit of toughness but quite enjoyable and rewarding.

By Daniel M

•Jan 06, 2019

A great course

By Cheng H

•Jan 23, 2019

best math course i've had so far after long years out of school~ thanks!

By 胡启阳

•Feb 19, 2019

Really helpful

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