このコースについて
4.8
124件の評価
26件のレビュー

100%オンライン

自分のスケジュールですぐに学習を始めてください。

柔軟性のある期限

スケジュールに従って期限をリセットします。

約18時間で修了

推奨:6-8 hours/week...

英語

字幕:英語

100%オンライン

自分のスケジュールですぐに学習を始めてください。

柔軟性のある期限

スケジュールに従って期限をリセットします。

約18時間で修了

推奨:6-8 hours/week...

英語

字幕:英語

シラバス - 本コースの学習内容

1
2時間で修了

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件のビデオ (合計53分), 2 readings, 5 quizzes
4件のビデオ
Sequences14 分
BONUS!5 分
Differences17 分
Discrete Calculus16 分
2件の学習用教材
Your Guide to Getting Started in this Course10 分
How Grading Works10 分
5の練習問題
Core Homework: Sequences14 分
Core Homework: Differences12 分
Challenge Homework: Differences8 分
Core Homework: Discrete Calculus10 分
Challenge Homework: Discrete Calculus4 分
2
1時間で修了

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件のビデオ (合計34分), 1 quiz
2件のビデオ
Numerical Integration16 分
1の練習問題
Core Homework: Numerical O.D.E.s4 分
3
2時間で修了

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件のビデオ (合計65分), 6 quizzes
4件のビデオ
Convergence Tests I16 分
Convergence Tests II16 分
Absolute & Conditional14 分
6の練習問題
Core Homework: Infinite Series10 分
Challenge Homework: Infinite Series4 分
Core Homework: Convergence Tests I16 分
Challenge Homework: Convergence Tests I4 分
Core Homework: Convergence Tests II6 分
Core Homework: Absolute & Conditional4 分
4
2時間で修了

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件のビデオ (合計59分), 5 quizzes
4件のビデオ
Taylor Series Redux15 分
Approximation and Error17 分
BONUS!9 分
5の練習問題
Core Homework: Power Series12 分
Challenge Homework: Power Series8 分
Core Homework: Taylor Series Redux8 分
Challenge Homework: Taylor Series Redux4 分
Core Homework: Approximation and Error10 分
4.8
26件のレビューChevron Right

人気のレビュー

by 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.

by 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

ペンシルベニア大学(University of Pennsylvania)について

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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