About this Course
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지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

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일정에 따라 마감일을 재설정합니다.

완료하는 데 약 18시간 필요

권장: 6-8 hours/week...

영어

자막: 영어

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

유동적 마감일

일정에 따라 마감일을 재설정합니다.

완료하는 데 약 18시간 필요

권장: 6-8 hours/week...

영어

자막: 영어

강의 계획 - 이 강좌에서 배울 내용

1
완료하는 데 2시간 필요

A Calculus for Sequences

It's time to redo calculus! Previously, all the calculus we have done is meant for functions with a continuous input and a continuous output. This time, we are going to retool calculus for functions with a <i>discrete</i> input. These are <i>sequences</i>, and they will occupy our attention for this last segment of the course. This first module will introduce the tools and terminologies for <b>discrete calculus</b>.

...
4 videos (Total 53 min), 2 readings, 5 quizzes
4개의 동영상
BONUS!5m
Differences17m
Discrete Calculus16m
2개의 읽기 자료
Your Guide to Getting Started in this Course10m
How Grading Works10m
5개 연습문제
Core Homework: Sequences14m
Core Homework: Differences12m
Challenge Homework: Differences8m
Core Homework: Discrete Calculus10m
Challenge Homework: Discrete Calculus4m
2
완료하는 데 1시간 필요

Introduction to Numerical Methods

That first module might have seemed a little...strange. It was! In this module, however, we will put that strangeness to good use, by giving a very brief introduction to the vast subjects of <b>numerical analysis</b>, answering such questions as <i>"how do we approximate solutions to differential equations?"</i> and <i>"how do we approximate definite integals?"</i> Perhaps unsurprisingly, Taylor expansion plays a pivotal role in these approximations.

...
2 videos (Total 34 min), 1 quiz
2개의 동영상
Numerical Integration16m
1개 연습문제
Core Homework: Numerical O.D.E.s4m
3
완료하는 데 2시간 필요

Series and Convergence Tests

In "ordinary" calculus, we have seen the importance (and challenge!) of improper integrals over unbounded domains. Within discrete calculus, this converts to the problem of infinite sums, or <b>series</b>. The determination of convergence for such will occupy our attention for this module. I hope you haven't forgotten your big-O notation --- you are going to need it!

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4 videos (Total 65 min), 6 quizzes
4개의 동영상
Convergence Tests I16m
Convergence Tests II16m
Absolute & Conditional14m
6개 연습문제
Core Homework: Infinite Series10m
Challenge Homework: Infinite Series4m
Core Homework: Convergence Tests I16m
Challenge Homework: Convergence Tests I4m
Core Homework: Convergence Tests II6m
Core Homework: Absolute & Conditional4m
4
완료하는 데 2시간 필요

Power and Taylor Series

This course began with an exploration of Taylor series -- an exploration that was, sadly, not as rigorous as one would like. Now that we have at our disposal all the tests and tools of discrete and continuous calculus, we can finally close the loop and make sense of what we've been doing when we Talyor-expand. This module will cover power series in general, from we which specify to our beloved Taylor series.

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4 videos (Total 59 min), 5 quizzes
4개의 동영상
Taylor Series Redux15m
Approximation and Error17m
BONUS!9m
5개 연습문제
Core Homework: Power Series12m
Challenge Homework: Power Series8m
Core Homework: Taylor Series Redux8m
Challenge Homework: Taylor Series Redux4m
Core Homework: Approximation and Error10m
4.9
27개의 리뷰Chevron Right

Single Variable Calculus의 최상위 리뷰

대학: MMJan 11th 2016

This course is tricky and also excellent. I am a computer science student from germany, and it took me quite some time and effort to pass it. The course is well structured, and can be done in time.

대학: RBFeb 11th 2017

Feeling really great after finishing the course. Learnt a lot and gained deeper insights into the calculus.\n\nLooking forward to Multi Variable Calculus.

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.

  • 수료증을 구매하면 성적 평가 과제를 포함한 모든 강좌 자료에 접근할 수 있습니다. 강좌를 완료하면 전자 수료증이 성취도 페이지에 추가되며, 해당 페이지에서 수료증을 인쇄하거나 LinkedIn 프로필에 수료증을 추가할 수 있습니다. 강좌 콘텐츠만 읽고 살펴보려면 해당 강좌를 무료로 청강할 수 있습니다.

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