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
課程信息
24,282 次近期查看
您將獲得的技能
Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution
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完成時間大約為24 小時
建議：6-8 hours/week
英語（English）
字幕：英語（English）, 西班牙語（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.
教學大綱 - 您將從這門課程中學到什麼
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.
完成時間為 3 小時
5 個視頻 （總計 75 分鐘）, 2 個閱讀材料, 8 個測驗
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
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.
完成時間為 2 小時
6 個視頻 （總計 76 分鐘）
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
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.
完成時間為 1 小時
3 個視頻 （總計 46 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
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.
完成時間為 2 小時
4 個視頻 （總計 50 分鐘）, 1 個閱讀材料, 6 個測驗
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
審閱
4.8
來自CALCULUS: SINGLE VARIABLE PART 3 - INTEGRATION的熱門評論
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.
由 VL 提供Jul 23, 2017
Some sections were too hard with limited information from the videos. I had to study other material to be able to complete them.
由 AK 提供Apr 25, 2017
I have really enjoyed learning materials from this course. This is a great chapter!
由 BP 提供Dec 8, 2016
excellent course ..please guys enroll and learn with best prof...Robert Ghrist....
由 JP 提供Apr 25, 2018
Just superb, not easy, challenging but so well prepared. Thanks for it Dr Ghrist.
由 RB 提供Feb 7, 2017
I will be sad when I finish Chapter 5. Cant wait for Multi variable calculus
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