About this Course
최근 조회 10,715

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

유동적 마감일

일정에 따라 마감일을 재설정합니다.

완료하는 데 약 22시간 필요

권장: 6-8 hours/week...

영어

자막: 영어, 스페인어

귀하가 습득할 기술

Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

유동적 마감일

일정에 따라 마감일을 재설정합니다.

완료하는 데 약 22시간 필요

권장: 6-8 hours/week...

영어

자막: 영어, 스페인어

강의 계획 - 이 강좌에서 배울 내용

1
완료하는 데 3시간 필요

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 videos (Total 75 min), 2 readings, 8 quizzes
5개의 동영상
A Simple O.D.E.16m
More O.D.E.s15m
O.D.E. Linearization16m
BONUS!8m
2개의 읽기 자료
How Grading Works10m
Your Guide to Getting Started in this Course10m
8개 연습문제
Core Homework: Indefinite Integrals10m
Challenge Homework: Indefinite Integrals2m
Core Homework: A Simple O.D.E.10m
Challenge Homework: A Simple O.D.E.4m
Core Homework: More O.D.E.s10m
Challenge Homework: More O.D.E.s8m
Core Homework: O.D.E. Linearization14m
Challenge Homework: O.D.E. Linearization6m
2
완료하는 데 2시간 필요

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 videos (Total 76 min), 8 quizzes
6개의 동영상
Integration by Parts16m
Trig Substitution15m
BONUS!7m
Partial Fractions15m
BONUS!6m
8개 연습문제
Core Homework: Integration by Substitution12m
Challenge Homework: Integration by Substitution4m
Core Homework: Integration by Parts14m
Challenge Homework: Integration by Parts6m
Core Homework: Trig Substitution12m
Challenge Homework: Trig Substitution6m
Core Homework: Partial Fractions12m
Challenge Homework: Partial Fractions6m
3
완료하는 데 1시간 필요

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.

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3 videos (Total 46 min), 3 quizzes
3개의 동영상
The F.T.I.C.16m
BONUS!12m
3개 연습문제
Core Homework: Definite Integrals10m
Core Homework: The F.T.I.C.10m
Challenge Homework: The F.T.I.C.8m
4
완료하는 데 2시간 필요

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.

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4 videos (Total 50 min), 1 reading, 6 quizzes
4개의 동영상
BONUS!6m
Trigonometric Integrals15m
Tables and Software11m
1개의 읽기 자료
About the Chpater 3 Exam10m
6개 연습문제
Core Homework: Improper Integrals16m
Challenge Homework: Improper Integrals10m
Core Homework: Trigonometric Integrals12m
Challenge Homework: Trigonometric Integrals4m
Challenge Homework: Tables and Software8m
Chapter 3: Integration - Exam20m
4.9
31개의 리뷰Chevron Right

Calculus: Single Variable Part 3 - Integration의 최상위 리뷰

대학: 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.

대학: 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.

강사

Avatar

Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

펜실베이니아 대학교 정보

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. ...

자주 묻는 질문

  • 강좌에 등록하면 바로 모든 비디오, 테스트 및 프로그래밍 과제(해당하는 경우)에 접근할 수 있습니다. 상호 첨삭 과제는 이 세션이 시작된 경우에만 제출하고 검토할 수 있습니다. 강좌를 구매하지 않고 살펴보기만 하면 특정 과제에 접근하지 못할 수 있습니다.

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