课程信息
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完成时间大约为18 小时

建议:6-8 hours/week...

英语(English)

字幕:英语(English)

100% 在线

立即开始,按照自己的计划学习。

可灵活调整截止日期

根据您的日程表重置截止日期。

完成时间大约为18 小时

建议:6-8 hours/week...

英语(English)

字幕:英语(English)

教学大纲 - 您将从这门课程中学到什么

1
完成时间为 2 小时

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>....
4 个视频 (总计 53 分钟), 2 个阅读材料, 5 个测验
4 个视频
Sequences14分钟
BONUS!5分钟
Differences17分钟
Discrete Calculus16分钟
2 个阅读材料
Your Guide to Getting Started in this Course10分钟
How Grading Works10分钟
5 个练习
Core Homework: Sequences14分钟
Core Homework: Differences12分钟
Challenge Homework: Differences8分钟
Core Homework: Discrete Calculus10分钟
Challenge Homework: Discrete Calculus4分钟
2
完成时间为 1 小时

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....
2 个视频 (总计 34 分钟), 1 个测验
2 个视频
Numerical Integration16分钟
1 个练习
Core Homework: Numerical O.D.E.s4分钟
3
完成时间为 2 小时

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!...
4 个视频 (总计 65 分钟), 6 个测验
4 个视频
Convergence Tests I16分钟
Convergence Tests II16分钟
Absolute & Conditional14分钟
6 个练习
Core Homework: Infinite Series10分钟
Challenge Homework: Infinite Series4分钟
Core Homework: Convergence Tests I16分钟
Challenge Homework: Convergence Tests I4分钟
Core Homework: Convergence Tests II6分钟
Core Homework: Absolute & Conditional4分钟
4
完成时间为 2 小时

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. ...
4 个视频 (总计 59 分钟), 5 个测验
4 个视频
Power Series16分钟
Taylor Series Redux15分钟
Approximation and Error17分钟
BONUS!9分钟
5 个练习
Core Homework: Power Series12分钟
Challenge Homework: Power Series8分钟
Core Homework: Taylor Series Redux8分钟
Challenge Homework: Taylor Series Redux4分钟
Core Homework: Approximation and Error10分钟
4.8
27 个审阅Chevron Right

热门审阅

创建者 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.

创建者 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.

讲师

Avatar

Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

关于 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. ...

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