Volver a 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....

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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por Mubashir-Ul-Hassan

•Aug 06, 2019

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

por Raghu P

•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. :)

por Luoqi W

•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.

por Thairo M T d S

•Jan 10, 2017

É incrível ter a experiência de poder realizar um curso tão rico e bem fundamentado de cálculo. Desde o começo, há uma ligação entre os assuntos, descobrindo não como ocorre em algumas aulas de cálculo que certos teoremas "saem da cartola" como mágica, e sim com a ajuda de algumas equações que, a partir do desenvolvimento algébrico delas, abrem o universo das séries de taylor. O que, sem dúvida, culmina na excelente demonstração do lim x->0 (sen x)/x e de L'Hopital.

Porém, é necessário, como o prof. G diz, já ter visto cálculo e ter uma certa maturidade. Recomendo fortemente um caderno ou um bloco de anotações, será bastante útil tanto como recordação ou como material para revisar. Excelente curso!

por Nachiket D

•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!

por Kumail A H

•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!

por Omar H

•Mar 09, 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 !

por Mrunmoy S

•Jan 11, 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!

por John C

•Jun 03, 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.

por Michael R

•Oct 01, 2019

I found it very enjoyable and challenging. A lot of effort has been put into its production and the questions test your understanding properly. Its not a beginners course, but it is doable if you have a reasonable grasp of calculus to begin with. I am looking forward to working through the multi-variable calculus ebooks and videos (aka calculus blue) that have been released (not on coursera). Good luck on this course, it is worth the effort.

por Naveen G

•May 13, 2020

Thanks to Prof. Ghrist and team for this wonderful (and of course challenging) course. This course helped me review calculus differently through the use of Taylor series. The problems composed for the quiz were challenging and fun. Although some concepts like Big O could have been explained better (personal opinion), the course lived up to its promise.

I'm truly grateful to Coursera for making this quality course available on the platform.

por Yakovenko I

•Apr 17, 2020

Very informative and insightful course. Visualisations and overall presentation are outstanding. Course material is provided in an innovative way and can be a perfect addition to a classic rigorous calculus course. Many real-life and beautiful examples are given, which support motivation and interest to move further along the course. However some prerequisite knowledge in calculus is required to fully enjoy the course material.

por Chris F

•Nov 05, 2017

I found this course to be very stimulating. It has been a while since I have studied Calculus. I took it a while ago and also have taught it but this is wonderful and frustrating at the same time. Some things you think you know, you need to go deeper . The use of the Taylor Series was interesting and for me different, but I see how it all comes into play and am looking forward to other sections that w ill hopefully follow.

por C M

•Oct 01, 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!

por Gabriel Q

•Sep 12, 2018

a great course to look at calculus in a different perspective, prof ghrist became one of my fav teachers as he paint with a subtle beauty the mathemathics he explains i'm thrilled to continue this journey of math thanks to him, and this is probably the go to class to expand and deepen on the wonderfull world of Taylor series and a functions in general, also free quizzes, lots of them!

por Albert Z

•Mar 03, 2020

Very great course! It was nice to be able to refresh AB and BC Calculus material after having not touched it for a year. In addition to reviewing what I already knew, this class featured additional information about calculus that was brand new to me. Every lecture taught me something I had not already known before. I feel prepared for what comes ahead in college mathematics now!

por Gregorio A A P

•Jul 08, 2017

Excelente, felicitaciones , solo que es triste no poder disfrutar al 100% un curso de esta calidad al no estar traducido al español, le agradecería que por favor lo traduzca del ingles al idioma español ya que solo esta parcialmente traducido.

nuevamente felicitaciones por la gran didáctica con la que imparte el curso y sobre todo por la calidad con la que enseña.

por 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/).

por Hemant P

•Jul 01, 2017

This course really helped me push my limits(forgive the pun) with highschool math. It was challenging but not so much that it demotivated me! Moreover, I watched many lectures twice and thrice and tried replicating the examples demonstrated in each lecture. It really helped me drill in the fundamentals I needed. I can proudly say I know Taylor Series now!

por Макарова Ю А

•Apr 02, 2020

Very nice course. I've been searching for a calculus course for some time as I want to try a completely new sphere for me and I needed something just above school program, but also not too advances as I graduated from school 10 years ago and don't remember everything. I am really grateful for these lectures and tasks, it was actually fun. Thank you!

por Hoagy C

•Sep 30, 2017

Very well explained, well set out, interesting concepts - highly recommended. Would have liked it if the 'Challenge' question sets were a little more thought provoking rather than (often) just requiring more computation - there were some interesting ones (the ln(lnx) question comes to mind) but didn't add as much depth as they could have.

por Darleen J T S

•May 18, 2020

A very useful course to reinforce and measure your knowledge of simple variable calculus at the level of functions, limits and Taylor series. I especially thank the teacher R. Ghrist and his collaborators for the didactic material that they have given us as well as for the challenging problems that they have posed to solve.

por Patrick S H

•Oct 05, 2019

I really appreciate the work that Professor Ghrist and the online curriculum team have put into making classes like this so accessible. I didn't feel like I was up to my knees in spam-can explanations, and just left to my own devices. Professor Ghrist is actually a very good tour guide for some very interesting territory.

por Oktarian T

•Dec 20, 2019

Amazing course, taught by a brilliant professor. A very useful course for me, as my previous calculus experience did not include Taylor Series. The homework took me a lot of time though, always over an hour. I didn't always manage the challenge homework. Overall very satisfied and looking forward to the next part.

por Shaurya A

•Jun 04, 2020

Course overall was great. The Professor Robert Greist explained wonderfully and the animation was also great. But there was a gap in the understanding about the big O and asymptotics specifically in week 4 lecture : Orders of growth

But everything else went in a great flow.

Looking forward to calculus 2

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