Back to Calculus: Single Variable Part 1 - Functions

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2,130 ratings

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.

Thank you so much Prof. Ghrist.

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By Matthieu B

â€¢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 C M

â€¢Sep 30, 2018

This has been a fantastic introduction to Calculus, albeit Taylor Series are not generally the first topic, but it is doable for someone who has already taken a basic Calculus course in college or high school. The exercises were challenging a lot of times, and I had to retake a lot of the quizzes. I studied thoughtfully and the result has been very pleasing. Looking forward to the next course!

By Taeho K

â€¢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 Dmitry E B

â€¢Sep 27, 2021

It is an extremely well prepared course, as Prof. Ghrist selected essentials of mathematics, concisely explained it in a concise manner, and provides well-selected exercises & answers to test the understanding and direct to misunderstood bits of the theory.

By Eskinder T

â€¢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 Rene G

â€¢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 Chinmay S

â€¢Jun 2, 2021

Excellent course! Prof. Ghrist is a great teacher. The examples in lectures and homework problems are very useful in understanding the concepts. Try to work on all the problems even if some may be challenging.

By K.S.S.UDUPA

â€¢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

â€¢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

â€¢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

â€¢Jul 24, 2019

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

By Ng T E

â€¢Nov 13, 2020

Very challenging course, even for a Calculus enthusiast like me

By warren t

â€¢Feb 23, 2022

Great course! Not for beginners!

By kathleensa

â€¢Jul 22, 2019

wonderful experince

By Robert A

â€¢Nov 17, 2020

Good course, but definitely difficult. A couple of quiz questions that were misleading or wrong.

By Mubashir-Ul-Hassan

â€¢Aug 6, 2019

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

By Kevin S

â€¢Nov 14, 2023

The supporting forum information is needed to be successful in this class, but the link to the forum is dead. I was able to do a web search and find a pdf of the forum information. That needs to be included in the course.

By Adam B

â€¢May 12, 2020

It would be helpful for the instructor to include more example in the lectures. The lectures are well taught and communicated, but there needs to be more emphasis on examples and how complicated some of the problems can be.

By Emil H

â€¢Feb 15, 2016

The lecturer wasn't very engaging. I gave up and continued with Ohio's Calculus course instead.

By fadi E

â€¢Apr 24, 2020

The course is heavily based on personal effort and not on explanation from the instructor. The course forced me to take more searches in the internet and find wonderful sites and tools related to the taylor series.

By rverker

â€¢Jan 4, 2024

The 15 minute videos only skim over the topics. If you don't have the basic math or have forgotten it, you will be wasting your time with this course. Additionally, there is no pdf support. Exercises that are not at all related to the examples given in the course. An example: you are asked for the Taylor series (yes, this course only talks about that) of the "sec" function without this function having been presented in the course. These exercises will require a lot of tedious calculation effort which will provide you with little additional knowledge. Imagine that you were asked to manually divide decimal numbers: what would you do? I bet you would use a calculator... Do the same with these exercises. I give 1 point because the guy is well dressed

By Deleted A

â€¢Jul 30, 2020

What a ridiculous course?!?! Hey guys, who did just rate it 5, I don't get at all!!! If you are reading this negative comments in order to understand wether to enrol, don't this!!! A little short video and a supercomplicated homework.

Isn't it strange assumption to assume, that the student already knows almost whole Calculus?

Just the waste of two precious days in my life, I could spend much much better!

The only thing I got from this course, I have to review my precalculus and I do not have so good Calculus basics as I thought!

I'd like to ask professor, who this course is for? I will go to Krista King to udemy instead.

HEY, DON'T WASTE YOUR TIME!!!

By (Lain) L P

â€¢Nov 29, 2021

While in this class I am having trouble actually learning much of anything. There are no example problems to work through and the Core Homework quizzes have little to nothing to do with the lecture. It would be incredibly beneficial for me to recieve some form of examples or homework.

By Deleted A

â€¢Apr 8, 2024

How can a professor, who is genius at Calculus, fail so badly at simple logic? I will quote him, "In order to success at this [calculus course], you must know basic calculus." What the heck is that supposed to mean? How can a class be its own prerequisite? DO NOW WASTE YOUR TIME!

By Tone M

â€¢May 22, 2020

15 minute cartoon then some unrelated problems?

No thanks