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.
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Calculus: Single Variable Part 1 - Functions
ペンシルベニア大学（University of Pennsylvania）このコースについて
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英語
字幕：アラビア語, フランス語, ポルトガル語（ヨーロッパ）, 中国語（簡体）, イタリア語, ベトナム語, ドイツ語, ロシア語, 英語, スペイン語
習得するスキル
- Series Expansions
- Calculus
- Series Expansion
柔軟性のある期限
スケジュールに従って期限をリセットします。
100%オンライン
自分のスケジュールですぐに学習を始めてください。
約14時間で修了
英語
字幕：アラビア語, フランス語, ポルトガル語（ヨーロッパ）, 中国語（簡体）, イタリア語, ベトナム語, ドイツ語, ロシア語, 英語, スペイン語
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ペンシルベニア大学（University of Pennsylvania）
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.
シラバス - 本コースの学習内容
1時間で修了
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...
1時間で修了
1件のビデオ （合計8分）, 2 学習用教材, 1 個のテスト
3時間で修了
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?
3時間で修了
3件のビデオ （合計36分）, 1 学習用教材, 4 個のテスト
5時間で修了
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....
5時間で修了
5件のビデオ （合計69分）
5時間で修了
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.
5時間で修了
4件のビデオ （合計62分）, 1 学習用教材, 7 個のテスト
レビュー
CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS からの人気レビュー
YGにより2018年7月2日
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.
NLにより2021年2月9日
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.
NKにより2016年2月22日
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.
KRにより2020年8月17日
Very good and challenging material! This motivated me to do better in my Calculus Courses. Would definitely have more of these courses soon, as this is suited for higher mathematics in college.
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