Back to Calculus: Single Variable Part 1 - Functions

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1,856 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 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

Eâ€‹xcellent 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 Bina S

â€¢Mar 6, 2021

Awesome , I love to do maths ( challenging maths ) like we are playing game and clearing level one by one ,but still it will be better if we get answer of question which we failed to attempt it

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 Arthur G

â€¢Oct 4, 2020

Much of the couse is good but the Homework test for Exponentials is attrocious.

Firstly the person setting it needs to learn English. Questions 6 & 7 say "which of the following expressions *describes ..." *
describes is the singular form of the verb and leads one to expect only
one expression applies. I did these questions twice being marked wrong
because I had only included one answer It needs altering to
"describe".

There are 2 correct answers listed for the first question but the marking system does not recognise one of them,

Question 8 again expects 2 answers but does not indicate there is more than one.

I did this test twice getting 50% but on realising these weaknesses i had no problem getting 100% but resdent wasting a whole morning because of your errors.

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 E H

â€¢Feb 15, 2016

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

By Raghu P

â€¢Apr 19, 2020

This course gives a completely different perspective of calculus, which we thought we had already learnt in our colleges. Professor Robert Ghrist explains the finer aspects of analysis of mathematical series. In fact, this course starts with Taylor Series, which is usually taught at the fag end of the undergraduate courses of Calculus. The capability to expand a function into Taylor Series, and then manipulating just enough number of its items to get our results; expanding Trigonometric, Exponential and Hyperbolic functions to make them amenable to mathematical analysis we want to do, etc. have been the main focus area of this course. It is not an easy course to take if you are not fully mathematics oriented. I was not. And that's why I had to spend hours and hours trying to figure out how the homework problems can be solved. Solving those problems gave different perspectives of the beauty of mathematics, which we might have ignored while studying to acquire just a degree in mathematics. Thank you, Professor Ghrist. :)

By Luoqi W

â€¢Aug 30, 2017

Absolutely phenomenal class. Prof. G leads the students in a tasteful exploration into the world of calculus with a curious heart and methodical mind. Lectures are grouped into weeks as mini-series and usually begin with a thought-provoking question or statement. These are immediately followed up with definitions and principles that lay the ground for further examination. But fear not if abstractions aren't your expertise, an army of concrete examples accompany you every step along the way.

Personally I completed this course on Coursera the summer before I entered college in 2013 as an electrical engineering student. To my amazement, even today in 2017 after all those years' bombardment from college level courses I am still revisiting Single Variable Calculus and find it a fresh breeze of air. Thank you Professor G and your team for creating what will be remembered as not just a great math class but a wonderful intellectual adventure.

By Matthew R P

â€¢Jul 21, 2020

Although I've only taken calculus 1 before, beginner calculus, and many moons ago, I thought the visual pictures as well as examples provided were very helpful. Dr. Ghrist is right in the curriculum introduction to the course, it is very hard, at least for me. I had particular trouble with combined and substitution functions, possibly because I've never had it in a math course. But a friend explained them to me, and that made the difference to me. For me I wish professor Ghrist would have gone over those subjects more. Nevertheless, professor Ghrist visual examples really were good for substitution and combination functions when I understood them better. Overall, I understand why Dr. Ghrist had the order of subjects in the course. The course overall was good, albeit very hard.

By Thairo M T d S

â€¢Jan 9, 2017

Ã‰ incrÃvel ter a experiÃªncia de poder realizar um curso tÃ£o rico e bem fundamentado de cÃ¡lculo. Desde o comeÃ§o, hÃ¡ uma ligaÃ§Ã£o entre os assuntos, descobrindo nÃ£o como ocorre em algumas aulas de cÃ¡lculo que certos teoremas "saem da cartola" como mÃ¡gica, e sim com a ajuda de algumas equaÃ§Ãµes que, a partir do desenvolvimento algÃ©brico delas, abrem o universo das sÃ©ries de taylor. O que, sem dÃºvida, culmina na excelente demonstraÃ§Ã£o do lim x->0 (sen x)/x e de L'Hopital.

PorÃ©m, Ã© necessÃ¡rio, como o prof. G diz, jÃ¡ ter visto cÃ¡lculo e ter uma certa maturidade. Recomendo fortemente um caderno ou um bloco de anotaÃ§Ãµes, serÃ¡ bastante Ãºtil tanto como recordaÃ§Ã£o ou como material para revisar. Excelente curso!

By Nachiket D

â€¢Feb 15, 2020

I absolutely loved this course!! Dr. Ghrist is an amazing teacher -- I wish I had him for calculus in college! I am truly grateful for my newfound fundamental understanding of Taylor Series and the key contributions of the exponential function, which underlies so much of mathematics. On a personal note, this course has really prepared me well as I make the transition from aerospace engineering to graduate studies in climate and weather science, renewable energy, and robotics. It will be especially helpful in the areas of numerical/computational fluid-thermal dynamics and control systems engineering. On to Part 2!

By Kumail A H

â€¢May 22, 2017

Excellent course! Prior exposure to Calculus (familiarity with a couple famous derivatives and integrals) is helpful, but you're sure to learn much more than that in this course. I have deepened my understanding of limits (not just the notion of a limit, but working out limits is now more intuitive to me) and stuff like l'hopital's rule seems logical now.

Starting with infinite series, with contrast to leaving it at the end, which is the standard in such courses, was brilliant!

Highly recommended!

By Omar H

â€¢Mar 8, 2017

The perfect course for someone with the basic knowledge of calculus and doesn't want to spend much time on the boring basic concepts (I am grad. student and need some calculus review). It is a genius idea that this course started with convergence and Taylor series, it made my life easier and simplified so many other things. The only part that I struggled with was the big "O" notation part, I feel it needs more elaboration. Other than this, everything is great. Off to the next course !

By Alvaro U M

â€¢Jul 19, 2020

I will write in Spanish.

Me gustÃ³ mucho el curso, aunque lo encontrÃ© difÃcil para mÃ. HacÃa mÃ¡s de 40 aÃ±os que no veÃa estas materias, por lo que tuve que esforzarme y estudiar mucho. EncontrÃ© interesante el enfoque poco ortodoxo de comenzar con Taylor Expansions. Me habrÃa gustado que los apuntes de Penn Calc se hubiesen podido leer mejor ya que aparecen escritos como parte de un programa. Me siento muy satisfecho y en un par de semanas voy a seguir con la segunda parte.

By Mrunmoy S

â€¢Jan 10, 2020

This course was quite fun to go through. You need to know basics of differentiation and integration. Some of the key points that I learned are Taylor expansions, l'hopital's rule, limits and orders of growth and how to compare two functions using their orders. I absolutely enjoyed the assignments and challenges. Some of them were quite tough but going through discussion forums helped to get an idea about the approach to solve them.

Thank you for this Course!

By John C

â€¢Jun 3, 2020

A course that is best taken after already learning a fair bit of Calculus. I would suggest not taking this course until you have completed a first-semester course and are already somewhat familiar with integrals and summations. With all that said, despite feeling rather confident with my prior abilities, this course has greatly enriched my understanding of many topics in Calculus. It has given me strong tools that I had not been exposed to previously.

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