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 1 - Functions
宾夕法尼亚大学課程信息
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完成時間大約為14 小時
英語（English）
字幕：阿拉伯語（Arabic）, 法語（French）, （歐洲人講的）葡萄牙語, 中文（簡體）, 意大利語, 越南語, 德語（German）, 俄語（Russian）, 英語（English）, 西班牙語（Spanish）
您將獲得的技能
- Series Expansions
- Calculus
- Series Expansion
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14 小時
英語（English）
字幕：阿拉伯語（Arabic）, 法語（French）, （歐洲人講的）葡萄牙語, 中文（簡體）, 意大利語, 越南語, 德語（German）, 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 1 小時
Introduction
Welcome to Calculus: Single Variable! below you will find the course's diagnostic exam. if you like, please take the exam. you don't need to score a minimal amount on the diagnostic in order to take the course. but if you do get a low score, you might want to readjust your expectations: this is a very hard class...
完成時間為 1 小時
1 個視頻 （總計 8 分鐘）, 2 個閱讀材料, 1 個測驗
完成時間為 3 小時
A Review of Functions
This module will review the basics of your (pre-)calculus background and set the stage for the rest of the course by considering the question: just what <i>is</i> the exponential function?
完成時間為 3 小時
3 個視頻 （總計 36 分鐘）, 1 個閱讀材料, 4 個測驗
完成時間為 5 小時
Taylor Series
This module gets at the heart of the entire course: the Taylor series, which provides an approximation to a function as a series, or "long polynomial". You will learn what a Taylor series is and how to compute it. Don't worry! The notation may be unfamiliar, but it's all just working with polynomials....
完成時間為 5 小時
5 個視頻 （總計 69 分鐘）
完成時間為 5 小時
Limits and Asymptotics
A Taylor series may or may not converge, depending on its limiting (or "asymptotic") properties. Indeed, Taylor series are a perfect tool for understanding limits, both large and small, making sense of such methods as that of l'Hopital. To solidify these newfound skills, we introduce the language of "big-O" as a means of bounding the size of asymptotic terms. This language will be put to use in future Chapters on Calculus.
完成時間為 5 小時
4 個視頻 （總計 62 分鐘）, 1 個閱讀材料, 7 個測驗
審閱
- 5 stars80.22%
- 4 stars15.40%
- 3 stars2.26%
- 2 stars0.70%
- 1 star1.40%
來自CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS的熱門評論
由 YF 提供2020年9月19日
There were certain advanced concepts that could have had a better and clearer explanation such as the “big O”. But on the whole it was a very good course and very much recommendable.
由 JV 提供2020年6月1日
Very Informative course and easy to catch. Although knowledge on the subject is a prerequisite before taking this. Not advisable to those with no knowledge whatsoever in calculus.
由 KR 提供2020年8月17日
Very good and challenging material! This motivated me to do better in my Calculus Courses. Would definitely have more of these courses soon, as this is suited for higher mathematics in college.
由 NL 提供2016年10月27日
What can I say? It is so good that I watch the lectures when I have dinner alone. Prof Ghrist absolutely has presented calculus so well that it becomes such an entertainment!
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