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 3 - Integration
宾夕法尼亚大学課程信息
14,847 次近期查看
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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
- 5 stars86.86%
- 4 stars11.05%
- 3 stars1.38%
- 2 stars0.23%
- 1 star0.46%
來自CALCULUS: SINGLE VARIABLE PART 3 - INTEGRATION的熱門評論
由 VB 提供2020年2月17日
The examples and the problems chosen are very thought provoking - the knowledge gained is fully tested by solving these problems.
由 VV 提供2017年7月23日
Some sections were too hard with limited information from the videos. I had to study other material to be able to complete them.
由 SX 提供2020年9月10日
I learned a lot about integral.The course contains many knowledge.
由 AK 提供2017年4月25日
I have really enjoyed learning materials from this course. This is a great chapter!
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