返回到 Calculus: Single Variable Part 4 - Applications

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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 fourth part--part four of five--we cover computing areas and volumes, other geometric applications, physical applications, and averages and mass. We also introduce probability....

Jul 07, 2018

The course taught me about how calculus is used to explain probability and statistics. This is exactly what I need to began studying these areas.

Jun 23, 2016

this was simply an amazing course, perfect for my skill level and exactly what i needed to learn. Thank you for the opportunity.

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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 Michael C

•May 03, 2019

Great course.

創建者 Louis J C J

•Feb 15, 2019

There is lots of material covered but the course hangs together well.

創建者 Ricardo S L

•Apr 29, 2018

Great that prof does not feed you with a spoon, but makes you work to understand the content.

創建者 Jose D

•Jan 28, 2017

This is a very educational MOOC. It summarizes major topics very efficiently while making the presentation agile and interesting. It includes a number of really good and challenging quizzes and homeworks.

I really like it so far!!.

創建者 maunil c

•Jan 24, 2016

quite impressive

創建者 Zamir M

•May 27, 2016

Excellent examples and surprising relationship between the concepts!

創建者 Paul D

•Feb 13, 2017

Great course as always --- took me a while this time

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 Sachin M V

•Dec 10, 2016

Really its hard to complete as many questions are tricky, but now i feel very nice after completion.

創建者 HyoungJin J

•Jan 06, 2018

great...awesome lecture....his voice is little bit funny though...

創建者 CMC

•Jul 07, 2018

The course taught me about how calculus is used to explain probability and statistics. This is exactly what I need to began studying these areas.

創建者 Tuan H

•Nov 06, 2016

great!

創建者 Patricia B

•Jul 11, 2017

Best calculus course ever.

創建者 Lau C C C

•Apr 21, 2018

thank you very much

創建者 EDILSON S S O J

•Oct 13, 2017

Amazing!

創建者 gian d g

•Feb 03, 2017

Entertaining and well thought, it seamlessly concatenates many calculus ideas into one tight program. The treatment of the infinitesimal elements as being the focus of understanding every concept was brilliant. Professor Ghrist is indeed a fantastic tutor and guide.

創建者 Alex G

•Jun 23, 2016

this was simply an amazing course, perfect for my skill level and exactly what i needed to learn. Thank you for the opportunity.

創建者 Radoslaw J

•Mar 17, 2017

The best math course I've ever seen, and also the best MOOC. The presentation is stellar.

創建者 Georgios P

•Sep 11, 2018

Ahead of its time!

創建者 Rafael C

•Jun 17, 2019

I can fully comprehend the purpose of this part, application, but the contradiction is that for students majoring in business, sociology or whatever, we're not bothered about how calculus can be applied in physics or geometry. Only the last part of probability is of interest to me. So I would propose that this part should be redesigned for different fields of application instead of integrating all different disciplines into one part, cuz much of the whole offering will have no connection with my later study. Yet the content of the course itself is good.

創建者 Justin J

•Jun 20, 2018

Personally frustrating voice and severe lack of explanation on topics.