课程信息
4.8
193 个评分
30 个审阅
100% 在线

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

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(小时)

完成时间大约为21 小时

建议:6-8 hours/week...
可选语言

英语(English)

字幕:英语(English), 西班牙语(Spanish)

您将获得的技能

Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution
100% 在线

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

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(小时)

完成时间大约为21 小时

建议:6-8 hours/week...
可选语言

英语(English)

字幕:英语(English), 西班牙语(Spanish)

教学大纲 - 您将从这门课程中学到什么

1
完成时间(小时)
完成时间为 3 小时

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 个视频 (总计 75 分钟), 2 个阅读材料, 8 个测验
Video5 个视频
A Simple O.D.E.16分钟
More O.D.E.s15分钟
O.D.E. Linearization16分钟
BONUS!8分钟
Reading2 个阅读材料
How Grading Works10分钟
Your Guide to Getting Started in this Course10分钟
Quiz8 个练习
Core Homework: Indefinite Integrals10分钟
Challenge Homework: Indefinite Integrals2分钟
Core Homework: A Simple O.D.E.10分钟
Challenge Homework: A Simple O.D.E.4分钟
Core Homework: More O.D.E.s10分钟
Challenge Homework: More O.D.E.s8分钟
Core Homework: O.D.E. Linearization14分钟
Challenge Homework: O.D.E. Linearization6分钟
2
完成时间(小时)
完成时间为 2 小时

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 个视频 (总计 76 分钟), 8 个测验
Video6 个视频
Integration by Parts16分钟
Trig Substitution15分钟
BONUS!7分钟
Partial Fractions15分钟
BONUS!6分钟
Quiz8 个练习
Core Homework: Integration by Substitution12分钟
Challenge Homework: Integration by Substitution4分钟
Core Homework: Integration by Parts14分钟
Challenge Homework: Integration by Parts6分钟
Core Homework: Trig Substitution12分钟
Challenge Homework: Trig Substitution6分钟
Core Homework: Partial Fractions12分钟
Challenge Homework: Partial Fractions6分钟
3
完成时间(小时)
完成时间为 1 小时

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 个视频 (总计 46 分钟), 3 个测验
Video3 个视频
The F.T.I.C.16分钟
BONUS!12分钟
Quiz3 个练习
Core Homework: Definite Integrals10分钟
Core Homework: The F.T.I.C.10分钟
Challenge Homework: The F.T.I.C.8分钟
4
完成时间(小时)
完成时间为 2 小时

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 个视频 (总计 50 分钟), 1 个阅读材料, 6 个测验
Video4 个视频
BONUS!6分钟
Trigonometric Integrals15分钟
Tables and Software11分钟
Reading1 个阅读材料
About the Chpater 3 Exam10分钟
Quiz6 个练习
Core Homework: Improper Integrals16分钟
Challenge Homework: Improper Integrals10分钟
Core Homework: Trigonometric Integrals12分钟
Challenge Homework: Trigonometric Integrals4分钟
Challenge Homework: Tables and Software8分钟
Chapter 3: Integration - Exam20分钟

讲师

Avatar

Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

关于 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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