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.
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Calculus: Single Variable Part 3 - Integration
宾夕法尼亚大学課程信息
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立即開始，按照自己的計劃學習。
完成時間大約為17 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）
您將獲得的技能
- Differential Equations
- Integration By Parts
- Improper Integral
- Integration By Substitution
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17 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.
授課大綱 - 您將從這門課程中學到什麼
完成時間為 6 小時
Integrating Differential Equations
Our first look at integrals will be motivated by differential equations. Describing how things evolve over time leads naturally to anti-differentiation, and we'll see a new application for derivatives in the form of stability criteria for equilibrium solutions.
完成時間為 6 小時
5 個視頻 （總計 75 分鐘）, 2 個閱讀材料, 8 個測驗
完成時間為 5 小時
Techniques of Integration
Since indefinite integrals are really anti-derivatives, it makes sense that the rules for integration are inverses of the rules for differentiation. Using this perspective, we will learn the most basic and important integration techniques.
完成時間為 5 小時
6 個視頻 （總計 76 分鐘）
完成時間為 2 小時
The Fundamental Theorem of Integral Calculus
Indefinite integrals are just half the story: the other half concerns definite integrals, thought of as limits of sums. The all-important *FTIC* [Fundamental Theorem of Integral Calculus] provides a bridge between the definite and indefinite worlds, and permits the power of integration techniques to bear on applications of definite integrals.
完成時間為 2 小時
3 個視頻 （總計 46 分鐘）
完成時間為 4 小時
Dealing with Difficult Integrals
The simple story we have presented is, well, simple. In the real world, integrals are not always so well-behaved. This last module will survey what things can go wrong and how to overcome these complications. Once again, we find the language of big-O to be an ever-present help in time of need.
完成時間為 4 小時
4 個視頻 （總計 50 分鐘）, 1 個閱讀材料, 6 個測驗
審閱
來自CALCULUS: SINGLE VARIABLE PART 3 - INTEGRATION的熱門評論
由 CC 提供2018年7月1日
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.
由 XL 提供2017年11月21日
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.
由 JJ 提供2021年3月4日
Students should be able to use trig and calculus cheat sheets while working problems. I would suggest they be provided and approved by the instructor.
由 AB 提供2016年6月17日
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.
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