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.
提供方
Calculus: Single Variable Part 4 - Applications
宾夕法尼亚大学課程信息
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完成時間大約為21 小時
英語（English）
字幕：法語（French）, （歐洲人講的）葡萄牙語, 俄語（Russian）, 英語（English）, 西班牙語（Spanish）
可靈活調整截止日期
根據您的日程表重置截止日期。
100% 在線
立即開始，按照自己的計劃學習。
完成時間大約為21 小時
英語（English）
字幕：法語（French）, （歐洲人講的）葡萄牙語, 俄語（Russian）, 英語（English）, 西班牙語（Spanish）
提供方
宾夕法尼亚大学
The University of Pennsylvania (commonly referred to as Penn) is a private university, located in Philadelphia, Pennsylvania, United States. A member of the Ivy League, Penn is the fourth-oldest institution of higher education in the United States, and considers itself to be the first university in the United States with both undergraduate and graduate studies.
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完成時間為 6 小時
Computing Areas and Volumes
Having seen some calculus before, you may recall some of the motivations for integrals arising from area computations. We will review those classical applications, while introducing the core idea of this module -- a differential element. By computing area and volume elements, we will see how to tackle tough geometry problems in a principled manner.
完成時間為 6 小時
6 個視頻 （總計 78 分鐘）, 2 個閱讀材料, 8 個測驗
完成時間為 4 小時
Other Geometric Applications
There's more to geometry than just area and volume! In this module, we will take things "to the next level", ascending to higher dimensions. Coming back to the 3-d world, we will return to problems of length and area, but this time in the context of curves and surfaces. As always, the emphasis will be on how to construct the appropriate differential element for integrating.
完成時間為 4 小時
4 個視頻 （總計 66 分鐘）
完成時間為 3 小時
Physical Applications
There is so much more to applications of integrals than geometry! So many subjects, from physics to finance, have, at heart, the need for setting up and computing definite integrals. In this short but intense module, we will cover applications including work, force, torque, mass, and present & future value.
完成時間為 3 小時
3 個視頻 （總計 36 分鐘）
完成時間為 4 小時
Averages and Mass
There is a statistical aspect to integrals that has not yet been brought up in this course: integrals are ideal for computing averages. Motivated by physical problems of mass, centroid, and moments of inertia, we will cover applications of integrals to averages.
完成時間為 4 小時
5 個視頻 （總計 65 分鐘）
審閱
- 5 stars90.21%
- 4 stars7.65%
- 3 stars1.27%
- 2 stars0.42%
- 1 star0.42%
來自CALCULUS: SINGLE VARIABLE PART 4 - APPLICATIONS的熱門評論
由 RB 提供2017年2月8日
This is exhausting but in a very good way. Can wait to start Chapter 5.
由 LJ 提供2019年2月14日
There is lots of material covered but the course hangs together well.
由 RJ 提供2017年3月16日
The best math course I've ever seen, and also the best MOOC. The presentation is stellar.
由 HY 提供2020年3月9日
Simply awesome! I would love to learn the digital calculus and the multi-variate calculus online with professor Ghrist.\n\nThank you! Dr. Ghrist
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