課程信息
4.9
110 個評分
22 個審閱
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完成時間(小時)

完成時間大約為18 小時

建議:6-8 hours/week...
可選語言

英語(English)

字幕:英語(English)...
100% online

100% online

立即開始,按照自己的計劃學習。
可靈活調整截止日期

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(小時)

完成時間大約為18 小時

建議:6-8 hours/week...
可選語言

英語(English)

字幕:英語(English)...

教學大綱 - 您將從這門課程中學到什麼

1
完成時間(小時)
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>....
Reading
4 個視頻(共 53 分鐘), 2 個閱讀材料, 5 個測驗
Video4 個視頻
Sequences14分鐘
BONUS!5分鐘
Differences17分鐘
Discrete Calculus16分鐘
Reading2 個閱讀材料
Your Guide to Getting Started in this Course10分鐘
How Grading Works10分鐘
Quiz5 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
2
完成時間(小時)
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....
Reading
2 個視頻(共 34 分鐘), 1 個測驗
Video2 個視頻
Numerical Integration16分鐘
Quiz1 個練習
Core Homework: Numerical O.D.E.s4分鐘
3
完成時間(小時)
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!...
Reading
4 個視頻(共 65 分鐘), 6 個測驗
Video4 個視頻
Convergence Tests I16分鐘
Convergence Tests II16分鐘
Absolute & Conditional14分鐘
Quiz6 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
4
完成時間(小時)
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. ...
Reading
4 個視頻(共 59 分鐘), 5 個測驗
Video4 個視頻
Power Series16分鐘
Taylor Series Redux15分鐘
Approximation and Error17分鐘
BONUS!9分鐘
Quiz5 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
4.9
22 個審閱Chevron Right

熱門審閱

創建者 MMJan 11th 2016

This course is tricky and also excellent. I am a computer science student from germany, and it took me quite some time and effort to pass it. The course is well structured, and can be done in time.

創建者 RBFeb 11th 2017

Feeling really great after finishing the course. Learnt a lot and gained deeper insights into the calculus.\n\nLooking forward to Multi Variable Calculus.

講師

Avatar

Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

關於 University of Pennsylvania

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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