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.
Single Variable Calculus
宾夕法尼亚大学課程信息
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完成時間大約為8 小時
英語（English）
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可分享的證書
完成後獲得證書
100% 在線
立即開始，按照自己的計劃學習。
可靈活調整截止日期
根據您的日程表重置截止日期。
完成時間大約為8 小時
英語（English）
字幕：英語（English）
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.
教學大綱 - 您將從這門課程中學到什麼
完成時間為 2 小時
A Calculus for Sequences
It's time to redo calculus! Previously, all the calculus we have done is meant for functions with a continuous input and a continuous output. This time, we are going to retool calculus for functions with a <i>discrete</i> input. These are <i>sequences</i>, and they will occupy our attention for this last segment of the course. This first module will introduce the tools and terminologies for <b>discrete calculus</b>.
完成時間為 2 小時
4 個視頻 （總計 53 分鐘）, 2 個閱讀材料, 5 個測驗
2 個閱讀材料
Your Guide to Getting Started in this Course10分鐘
How Grading Works10分鐘
5 個練習
Core Homework: Sequences14分鐘
Core Homework: Differences12分鐘
Challenge Homework: Differences8分鐘
Core Homework: Discrete Calculus10分鐘
Challenge Homework: Discrete Calculus4分鐘
完成時間為 1 小時
Introduction to Numerical Methods
That first module might have seemed a little...strange. It was! In this module, however, we will put that strangeness to good use, by giving a very brief introduction to the vast subjects of <b>numerical analysis</b>, answering such questions as <i>"how do we approximate solutions to differential equations?"</i> and <i>"how do we approximate definite integals?"</i> Perhaps unsurprisingly, Taylor expansion plays a pivotal role in these approximations.
完成時間為 1 小時
2 個視頻 （總計 34 分鐘）
1 個練習
Core Homework: Numerical O.D.E.s4分鐘
完成時間為 2 小時
Series and Convergence Tests
In "ordinary" calculus, we have seen the importance (and challenge!) of improper integrals over unbounded domains. Within discrete calculus, this converts to the problem of infinite sums, or <b>series</b>. The determination of convergence for such will occupy our attention for this module. I hope you haven't forgotten your big-O notation --- you are going to need it!
完成時間為 2 小時
4 個視頻 （總計 65 分鐘）
6 個練習
Core Homework: Infinite Series10分鐘
Challenge Homework: Infinite Series4分鐘
Core Homework: Convergence Tests I16分鐘
Challenge Homework: Convergence Tests I4分鐘
Core Homework: Convergence Tests II6分鐘
Core Homework: Absolute & Conditional4分鐘
完成時間為 2 小時
Power and Taylor Series
This course began with an exploration of Taylor series -- an exploration that was, sadly, not as rigorous as one would like. Now that we have at our disposal all the tests and tools of discrete and continuous calculus, we can finally close the loop and make sense of what we've been doing when we Talyor-expand. This module will cover power series in general, from we which specify to our beloved Taylor series.
完成時間為 2 小時
4 個視頻 （總計 59 分鐘）
5 個練習
Core Homework: Power Series12分鐘
Challenge Homework: Power Series8分鐘
Core Homework: Taylor Series Redux8分鐘
Challenge Homework: Taylor Series Redux4分鐘
Core Homework: Approximation and Error10分鐘
審閱
來自SINGLE VARIABLE CALCULUS的熱門評論
由 PC 提供2019年9月14日
Loved it ! I've grown attached to Prof. Ghrist's lectures, so it is with a heavy heart that I took the final exam and finished this course. I xould really love to take another !
由 SC 提供2020年4月9日
A fantastic course. Kudos to Prof. Ghrist for making this a fun, interesting and challenging ride at the same time. Looking forward to Multivariable Calculus by Prof. Ghrist.
由 RB 提供2017年2月10日
Feeling really great after finishing the course. Learnt a lot and gained deeper insights into the calculus. Looking forward to Multi Variable Calculus.
由 XL 提供2017年12月3日
Again and again and again ... love the bonus lectures! Really enlightening! Please release the Multi-variable Calculus ASAP! Can't wait to take it!
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