Calculus: Single Variable Part 1 - Functions に戻る

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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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by 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!

by Kumail H 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!

by 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 !

by 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!

by 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.

by Yakovenko I

•Aug 27, 2018

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.

by 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.

by 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!

by 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!

by 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.

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 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!

by 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.

by 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.

by 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.

by Brian N A

•Jun 24, 2018

I enjoyed the course, and I will be taking the other parts of it too. The problems seem well designed to expose flaws in your thinking. I still feel somewhat shaky on some topics, but I would say the overall concepts came through very well, and the journey through them was cohesive and well laid-out.

by Taeho K

•Nov 05, 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 Mikayla B

•Jun 19, 2016

This course offers so much! I haven't been in a class that goes this in-depth in calculus. I definitely recommend this course to others who want to explore calculus and want a challenge!

Best of luck to those who choose to enroll in all 5 parts of single variable calculus sessions. It's worth it :)

by Carlos A

•May 03, 2017

It was great, the lectures were amazingly done, I loved all the colors and stuff made.

Clear and understandable.

Exercises not too hard, not too easy.

Our starting point is Euler's identity and Taylor Series, wich we take as a given. I didn't like it very much, but, overall, it accomplishes its goal.

by Don H

•Mar 02, 2019

It's not perfect, but no course is. This course won't raise your test scores (at least not immediately). To do that, you have to buckle down and study the material assigned by your professor. But if you want a deeper understanding of the concept, I couldn't recommend a better course or platform.

by michael f

•May 18, 2017

I thoroughly enjoyed this course. Prof. Ghrist is an excellent teacher. The course was a tad bit harder than i has expected it to be, but nonetheless, i thoroughly enjoyed it and would recommend it to anyone who has an interest in Mathematics and calculus. It also cleared some of my concepts.

by Valerie C

•Mar 07, 2016

I found this course to be very helpful, challenging, informative, and well-made. There was obvious a lot of time and effort put into making the videos. I have a good amount of math experience, but I still found it challenging and interesting. I'm very happy to have found this resource.

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 Aleksey C

•Dec 29, 2016

When I retake homework tasks I try to fix tasks I failed on previous attempt. IMHO it make sense to not repeat them all but provide only tasks that were solved incorrectly. Repeating ALL tasks just wastes my time for reentering correct answers and is error-prone process.

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.