課程信息
4.8
206 個評分
30 個審閱

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

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完成時間大約為22 小時

建議:6-8 hours/week...

英語(English)

字幕:英語(English), 西班牙語(Spanish)

您將獲得的技能

Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution

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22 小時

建議:6-8 hours/week...

英語(English)

字幕:英語(English), 西班牙語(Spanish)

教學大綱 - 您將從這門課程中學到什麼

1
完成時間為 3 小時

Integrating Differential Equations

Our first look at integrals will be motivated by differential equations. Describing how things evolve over time leads naturally to anti-differentiation, and we'll see a new application for derivatives in the form of stability criteria for equilibrium solutions....
5 個視頻 (總計 75 分鐘), 2 個閱讀材料, 8 個測驗
5 個視頻
A Simple O.D.E.16分鐘
More O.D.E.s15分鐘
O.D.E. Linearization16分鐘
BONUS!8分鐘
2 個閱讀材料
How Grading Works10分鐘
Your Guide to Getting Started in this Course10分鐘
8 個練習
Core Homework: Indefinite Integrals10分鐘
Challenge Homework: Indefinite Integrals2分鐘
Core Homework: A Simple O.D.E.10分鐘
Challenge Homework: A Simple O.D.E.4分鐘
Core Homework: More O.D.E.s10分鐘
Challenge Homework: More O.D.E.s8分鐘
Core Homework: O.D.E. Linearization14分鐘
Challenge Homework: O.D.E. Linearization6分鐘
2
完成時間為 2 小時

Techniques of Integration

Since indefinite integrals are really anti-derivatives, it makes sense that the rules for integration are inverses of the rules for differentiation. Using this perspective, we will learn the most basic and important integration techniques. ...
6 個視頻 (總計 76 分鐘), 8 個測驗
6 個視頻
Integration by Parts16分鐘
Trig Substitution15分鐘
BONUS!7分鐘
Partial Fractions15分鐘
BONUS!6分鐘
8 個練習
Core Homework: Integration by Substitution12分鐘
Challenge Homework: Integration by Substitution4分鐘
Core Homework: Integration by Parts14分鐘
Challenge Homework: Integration by Parts6分鐘
Core Homework: Trig Substitution12分鐘
Challenge Homework: Trig Substitution6分鐘
Core Homework: Partial Fractions12分鐘
Challenge Homework: Partial Fractions6分鐘
3
完成時間為 1 小時

The Fundamental Theorem of Integral Calculus

Indefinite integrals are just half the story: the other half concerns definite integrals, thought of as limits of sums. The all-important *FTIC* [Fundamental Theorem of Integral Calculus] provides a bridge between the definite and indefinite worlds, and permits the power of integration techniques to bear on applications of definite integrals. ...
3 個視頻 (總計 46 分鐘), 3 個測驗
3 個視頻
The F.T.I.C.16分鐘
BONUS!12分鐘
3 個練習
Core Homework: Definite Integrals10分鐘
Core Homework: The F.T.I.C.10分鐘
Challenge Homework: The F.T.I.C.8分鐘
4
完成時間為 2 小時

Dealing with Difficult Integrals

The simple story we have presented is, well, simple. In the real world, integrals are not always so well-behaved. This last module will survey what things can go wrong and how to overcome these complications. Once again, we find the language of big-O to be an ever-present help in time of need. ...
4 個視頻 (總計 50 分鐘), 1 個閱讀材料, 6 個測驗
4 個視頻
BONUS!6分鐘
Trigonometric Integrals15分鐘
Tables and Software11分鐘
1 個閱讀材料
About the Chpater 3 Exam10分鐘
6 個練習
Core Homework: Improper Integrals16分鐘
Challenge Homework: Improper Integrals10分鐘
Core Homework: Trigonometric Integrals12分鐘
Challenge Homework: Trigonometric Integrals4分鐘
Challenge Homework: Tables and Software8分鐘
Chapter 3: Integration - Exam20分鐘
4.8
30 個審閱Chevron Right

熱門審閱

創建者 CCJul 2nd 2018

I like it because it though me differential equations. This topics was previously missing from my education. It can be daunting to learn DE without proper guidance. This course provided just that.

創建者 ABJun 18th 2016

A bit difficult, but not truly when a good effort is made. No doubt interesting. Even a post graduate student will truly benefit from this course.

講師

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Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

關於 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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