課程信息
4.8
199 個評分
30 個審閱
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立即開始,按照自己的計劃學習。
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完成時間(小時)

完成時間大約為21 小時

建議:6-8 hours/week...
可選語言

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

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

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21 小時

建議:6-8 hours/week...
可選語言

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(小時)
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....
Reading
5 個視頻 (總計 75 分鐘), 2 個閱讀材料, 8 個測驗
Video5 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
Reading2 個閱讀材料
How Grading Works10分鐘
Your Guide to Getting Started in this Course10分鐘
Quiz8 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(小時)
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. ...
Reading
6 個視頻 (總計 76 分鐘), 8 個測驗
Video6 個視頻
Integration by Parts16分鐘
Trig Substitution15分鐘
BONUS!7分鐘
Partial Fractions15分鐘
BONUS!6分鐘
Quiz8 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(小時)
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. ...
Reading
3 個視頻 (總計 46 分鐘), 3 個測驗
Video3 個視頻
The F.T.I.C.16分鐘
BONUS!12分鐘
Quiz3 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(小時)
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. ...
Reading
4 個視頻 (總計 50 分鐘), 1 個閱讀材料, 6 個測驗
Video4 個視頻
BONUS!6分鐘
Trigonometric Integrals15分鐘
Tables and Software11分鐘
Reading1 個閱讀材料
About the Chpater 3 Exam10分鐘
Quiz6 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

講師

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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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