返回到 Calculus: Single Variable Part 3 - Integration

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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 third part--part three of five--we cover integrating differential equations, techniques of integration, the fundamental theorem of integral calculus, and difficult integrals....

Jul 02, 2018

I like it because it though me differential equations. This topics was previously missing from my education. It can be daunting to learn DE without proper guidance. This course provided just that.

Nov 22, 2017

The Bonus lectures are just great! I majored in Mathematics in university, and they're even enlightening to me. BTW, thanks for the introduction to Wolfram Alpha. It's really fun.

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創建者 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.

創建者 Omar J

•Nov 10, 2018

So far the most difficult chapter of the 5-part calculus course. This makes successfully finishing the course feel like a great achievement. Prof. Ghrist does a wonderful job explaining the concepts of this chapter. The structure of the course is also well-organized to gradually give the learner a better understanding of integration concepts and techniques.

創建者 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.

創建者 Guillermo A

•Apr 18, 2020

As usual, Prof. Grist courses are outstanding.

I found this one a bit more difficult for comfort. A few times I felt like having hit a brick wall and couldn't go forward. I had to review the sessions multiple times. However, it was sure worth the suffering.

Looking for for the next one.

創建者 John H

•Apr 14, 2020

This is an excellent course, giving a super, in-depth, coverage of Integration. I love Professor Ghrist's presentation and the visuals are the best I have seen. Really good challenging exercises as well. Thanks.

創建者 Abd A A R E

•Jul 06, 2020

The way this course is taught is different from any classical way of teaching calculus. The course here is presenting the whole philosophy of calculus based on Taylor's series and this is really amazing.

創建者 CMC

•Jul 02, 2018

I like it because it though me differential equations. This topics was previously missing from my education. It can be daunting to learn DE without proper guidance. This course provided just that.

創建者 Xiao L

•Nov 22, 2017

The Bonus lectures are just great! I majored in Mathematics in university, and they're even enlightening to me. BTW, thanks for the introduction to Wolfram Alpha. It's really fun.

創建者 Abhijit B

•Jun 18, 2016

A bit difficult, but not truly when a good effort is made. No doubt interesting. Even a post graduate student will truly benefit from this course.

創建者 Vishu B

•Feb 18, 2020

The examples and the problems chosen are very thought provoking - the knowledge gained is fully tested by solving these problems.

創建者 Ann

•Aug 17, 2016

I having been previewing Calculus over the summer and have taken courses from different sources.THIS COURSE DOES HELPS THE MOST.

創建者 JORGE E M L V

•May 31, 2019

Excelente curso de verdad que es muy bueno hacerlo ya que se aprende mucho del cálculo integral en una variable

創建者 江祖榮

•Aug 02, 2019

Great lecture of integration with a tons of practical thought-provoking example and illustration.

創建者 Alassane K

•Apr 26, 2017

I have really enjoyed learning materials from this course. This is a great chapter!

創建者 Bhavik P

•Dec 09, 2016

excellent course ..please guys enroll and learn with best prof...Robert Ghrist....

創建者 Jorge P

•Apr 26, 2018

Just superb, not easy, challenging but so well prepared. Thanks for it Dr Ghrist.

創建者 杨佳熙

•Jun 21, 2016

the first four session is free which is econmic friendly. show u my respect :)

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創建者 Rene G

•Oct 10, 2019

top course,

if you think you know calculus, take this one for the next step !

創建者 Rohit B

•Feb 08, 2017

I will be sad when I finish Chapter 5. Cant wait for Multi variable calculus

創建者 Achintya S

•May 07, 2020

Thank you, this was very helpful and helped me prepare for college !!

創建者 Илья

•Feb 11, 2020

more difficult than first 2 courses. But quality is same high

創建者 bernie3311

•Sep 10, 2017

a rather difficult one but clearly and simply explained.

創建者 Guo F

•Jul 30, 2020

Wonderful Course! Challenging in a nice way!

創建者 Nafis F

•Aug 08, 2020

No words to praise this course. NONE.

創建者 Мария Ш

•Mar 12, 2017

Where is the certificate? Thank you.