Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach.
提供方
Calculus: Single Variable Part 3 - Integration
宾夕法尼亚大学课程信息
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100% 在线
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完成时间大约为9 小时
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
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9 小时
英语（English）
字幕：英语（English）, 西班牙语（Spanish）
提供方
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.
教学大纲 - 您将从这门课程中学到什么
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.
完成时间为 3 小时
5 个视频 （总计 75 分钟）, 2 个阅读材料, 8 个测验
2 个阅读材料
How Grading Works10分钟
Your Guide to Getting Started in this Course10分钟
8 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
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.
完成时间为 2 小时
6 个视频 （总计 76 分钟）
6 个视频
Integration by Parts16分钟
Trig Substitution15分钟
BONUS!7分钟
Partial Fractions15分钟
BONUS!6分钟
8 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
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.
完成时间为 1 小时
3 个视频 （总计 46 分钟）
3 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
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.
完成时间为 2 小时
4 个视频 （总计 50 分钟）, 1 个阅读材料, 6 个测验
1 个阅读材料
About the Chpater 3 Exam10分钟
6 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
审阅
来自CALCULUS: SINGLE VARIABLE PART 3 - INTEGRATION的热门评论
由 CC 提供Jul 1, 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.
由 XL 提供Nov 21, 2017
The Bonus lectures are just great! I majored in Mathematics in university, and they're even enlightening to me. BTW, thanks for the introduction to Wolfram Alpha. It's really fun.
由 AB 提供Jun 17, 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.
由 VB 提供Feb 17, 2020
The examples and the problems chosen are very thought provoking - the knowledge gained is fully tested by solving these problems.
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