Single Variable Calculus 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 fifth part--part five of five--we cover a calculus for sequences, numerical methods, series and convergence tests, power and Taylor series, and conclude the course with a final exam. Learners in this course can earn a certificate in the series by signing up for Coursera's verified certificate program and passing the series' final exam....

Jan 11, 2016

This course is tricky and also excellent. I am a computer science student from germany, and it took me quite some time and effort to pass it. The course is well structured, and can be done in time.

Sep 15, 2019

Loved it ! I've grown attached to Prof. Ghrist's lectures, so it is with a heavy heart that I took the final exam and finished this course. I xould really love to take another !

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by Xiao L

•Dec 04, 2017

Again and again and again ... love the bonus lectures! Really enlightening! Please release the Multi-variable Calculus ASAP! Can't wait to take it!

by Sanchit S

•Aug 21, 2016

Hey guys. So I just completed a Discrete Calculus course, offered by UPenn, through Coursera. I'd like to give a you guys an overview of the course, and my experience through this journey.

This, 5 part course, is designed to be completed within 21 weeks, with a work time of 6-8 hours a week. However, if you're really dedicated and have enough time, you can probably finish it within 8 weeks (like me). Oh, and it is taught by Prof. Robert Ghrist (he's cool, trust me).

First, for the prerequisites, you should have taken at least Calculus AB, to do well in this course. Practice with advanced integration techniques and some prior knowledge of Taylor Series is a plus.

Part 1 of the course begins with a study of Taylor Series. From what I've noticed, part 1 emphasizes the importance of using Taylor Series to develop an intuition about the behavior of a function at limits such as 0 and infinity. After revisiting some familiar topics with the perspective of Taylor, part 1 ends with introducing asymptotic analysis (big O), which took me a while to grasp.

Part 2 is review for the most part. However, it helps to further strengthen the idea of differentials, and their uses. Some bonus lectures introduce topology, and spacial curvature. Also, there is an introduction to the algebra of operators (which is elaborated in part 5) Some BC topics are also reviewed.

Part 3 mostly deals with practicing integration techniques, however emphasizes on Differential Equations (with specific focus on coupled oscillators). Formal definite integrals are introduced. Some more BC topics are reviewed.

Part 4, focuses on applying knowledge from the preceding parts. Although it starts off easy with areas, volumes, and arc length, the focus shifts to statistics and physical applications. There is a weird study of Work. Rotational Inertia and PDFs are taught in tandem. There is a brief study of high dimension spaces and hyper volumes. Centroids are taught through the use of double integrals.

Finally, part 5 introduces discrete calculus. Basically, continuous calculus, retaught with the perspective of series, in a discretized, non continuous setting. It begins with the study of finite differences, and a rather comprehensive practice of discrete integration. Differential equations (aka recursion relations) are taught, through the use of operators. Then, the focus shifts to numerical analysis, by introducing methods to approximate integrals (like Runge Kutta method). Following that, there is a very comprehensive study of convergence of series. And trust me, it is taught super well (way more in-depth than BC). Finally, the focus shifts to the rather obscure Taylor Remainder Theorem. This might be review for some.

This course was pretty challenging for me. I spent a lot of time doing my homework, and taking really good notes (for future reference). After a fee of $50, I earned my course certificate after the final exam (sigh).

This is a super cool course.

by Khadija H

•Jan 31, 2019

Challenging but worth it! I did have to use supplemental tools to aid in my learning but that may not be the case for everyone.

by Mohammed A

•Jun 26, 2018

This was a great course. It was my first time learning about single-variable calculus with Taylor Series at the heart of it. It gave me a deeper and better perspective. It was also my first time learning about topics like orders of growth and big-oh, forward differences, Fibonacci and Pell sequences, falling powers and discrete calculus. I had a blast learning about them. The professor also introduced ODEs, probability, discrete mathematics and numerical methods. He got me interested in taking a course on each one of these subjects. The design and execution of the video lectures was excellent. Homework and exam problems were challenging and helped solidify my understanding of the material. Don't miss this course!

by Anna S

•Oct 16, 2017

An excellent course, very challenging, but doable and enjoyable. A lot of thanks to professor Ghrist and his team for the tremendous work on building this course and for my improved level of understanding Calculus. I have just started the university course of classical mechanics, and all problems incluling Calculus seem to be so easy after this tough training. Also a lot of thanks to all of the mentors, for their dedication, patience and and help. If the Multivariable Calculus course by this team becomes available, I definitely will be among its first students.

by Robert H

•Feb 03, 2017

That was a brilliant journey through Single Variable Calculus-land. Well done Prof G and team! Thanks for the ride.

by Rafael C

•Jul 21, 2019

HARD!!!

by Zhenan L

•Jul 30, 2019

Hard

by Nathan H

•Oct 12, 2018

There are assignments in this course that leave the student unprepared to pass based on the material. The discussion forums point to trying harder or using other methods, but offer little help. It looks as though students spend weeks on completing a single HW assignment. A simple format change would go a long way in testing the students' understanding while not just giving them the answer.

by Yang X

•Mar 06, 2016

This whole series is just amazing. It teaches Calculus in a way that's so different from how it is taught in most universities. I thought I would never be able to do Calculus but I was really successful after finishing the 5-course series in 2 months. Highly recommended

by Weinan H

•Aug 24, 2017

The course content is really satisfying. The difficulty in Challenges is quite cool while the homework problems and the tests are reasonable. I kind of of fell in love with math with Prof. Ghrist help.

by Maximilian N J W M

•Jan 11, 2016

This course is tricky and also excellent. I am a computer science student from germany, and it took me quite some time and effort to pass it. The course is well structured, and can be done in time.

by 高宇

•Mar 11, 2019

Although still confused with differential equation, I have made great pregross on calculus, and even mathmatics. This is another to watch the world and reconstruct my mind facing problems.

by Paul C

•Sep 15, 2019

Loved it ! I've grown attached to Prof. Ghrist's lectures, so it is with a heavy heart that I took the final exam and finished this course. I xould really love to take another !

by Rohit B

•Feb 11, 2017

Feeling really great after finishing the course. Learnt a lot and gained deeper insights into the calculus.

Looking forward to Multi Variable Calculus.

by kanagaratnam j

•Jun 06, 2016

It was very helpful to understand calculus and application.

this Vedio lesson and animation very helpfull.

by Ignacio M A

•Oct 08, 2017

Excellent set of courses! I really hope there will be a multivariable course in the same fashion.

by jonas m

•Jul 26, 2019

Great course, although quite challenging at parts. Nevertheless, the fruits are rewarding!

by Matthew J

•Jun 11, 2019

This fifth unit is highly original! I loved the "digital calculus" part.

by CMC

•Jul 10, 2018

An introduction to numerical analysis was exactly what I need.

by Georgios P

•Dec 20, 2017

A course from the future of education!

by Maarten B

•Sep 25, 2017

I would highly suggest trying it out!

by maunil c

•Jan 24, 2016

professor's explanation is the best.

by Adam R

•Jul 08, 2019

So helpful and makes math beautiful

by Patricia B

•Jul 11, 2017

Best calculus course ever.