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.
제공자:
Calculus: Single Variable Part 1 - Functions
펜실베이니아 대학교이 강좌에 대하여
최근 조회 40,393회
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영어
자막: 아랍어, 프랑스어, 포르투갈어 (유럽), 중국어 (간체자), 이탈리아어, 베트남어, 독일어, 러시아어, 영어, 스페인어
귀하가 습득할 기술
- Series Expansions
- Calculus
- Series Expansion
유연한 마감일
일정에 따라 마감일을 재설정합니다.
100% 온라인
지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.
완료하는 데 약 14시간 필요
영어
자막: 아랍어, 프랑스어, 포르투갈어 (유럽), 중국어 (간체자), 이탈리아어, 베트남어, 독일어, 러시아어, 영어, 스페인어
제공자:
펜실베이니아 대학교
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.
강의 계획표 - 이 강좌에서 배울 내용
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Introduction
Welcome to Calculus: Single Variable! below you will find the course's diagnostic exam. if you like, please take the exam. you don't need to score a minimal amount on the diagnostic in order to take the course. but if you do get a low score, you might want to readjust your expectations: this is a very hard class...
완료하는 데 1시간 필요
1개 동영상 (총 8분), 2 개의 읽기 자료, 1 개의 테스트
완료하는 데 3시간 필요
A Review of Functions
This module will review the basics of your (pre-)calculus background and set the stage for the rest of the course by considering the question: just what <i>is</i> the exponential function?
완료하는 데 3시간 필요
3개 동영상 (총 36분), 1 개의 읽기 자료, 4 개의 테스트
완료하는 데 5시간 필요
Taylor Series
This module gets at the heart of the entire course: the Taylor series, which provides an approximation to a function as a series, or "long polynomial". You will learn what a Taylor series is and how to compute it. Don't worry! The notation may be unfamiliar, but it's all just working with polynomials....
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5개 동영상 (총 69분)
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Limits and Asymptotics
A Taylor series may or may not converge, depending on its limiting (or "asymptotic") properties. Indeed, Taylor series are a perfect tool for understanding limits, both large and small, making sense of such methods as that of l'Hopital. To solidify these newfound skills, we introduce the language of "big-O" as a means of bounding the size of asymptotic terms. This language will be put to use in future Chapters on Calculus.
완료하는 데 5시간 필요
4개 동영상 (총 62분), 1 개의 읽기 자료, 7 개의 테스트
검토
CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS의 최상위 리뷰
YG 제공2018년 7월 2일
Very well structured for a refresher course. Thank you Professor Ghrist for your effort in putting this course together. A little additional outside research was required but well worth the effort.
NK 제공2016년 2월 22일
Would have preferred accompanying solutions. Just getting the answer ain't enough. Making sure my approach is correct is essential as well considering the course touches upon the absolute basics.
NL 제공2021년 2월 9일
Excellent introduction to Calculus, I wanted to review the material to tutor my child but I am very happy that I learned a whole new way of looking at Calculus. Thank you so much Prof. Ghrist.
BS 제공2021년 3월 5일
Awesome , I love to do maths ( challenging maths ) like we are playing game and clearing level one by one ,but still it will be better if we get answer of question which we failed to attempt it
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