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
宾夕法尼亚大学
课程信息
181,156 次近期查看
学生职业成果
35%
完成这些课程后已开始新的职业生涯
30%
通过此课程获得实实在在的工作福利
15%
加薪或升职
您将获得的技能
Series ExpansionsCalculusSeries Expansion
学生职业成果
35%
完成这些课程后已开始新的职业生涯
30%
通过此课程获得实实在在的工作福利
15%
加薪或升职
100% 在线
立即开始，按照自己的计划学习。
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完成时间大约为21 小时
建议：6-8 hours/week
英语（English）
字幕：英语（English）, 西班牙语（Spanish）, 中文（简体）
教学大纲 - 您将从这门课程中学到什么
完成时间为 1 小时
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...
完成时间为 1 小时
1 个视频 （总计 8 分钟）, 2 个阅读材料, 1 个测验
1 个视频
Introduction8分钟
2 个阅读材料
Welcome10分钟
Your Guide to Getting Started in this Course10分钟
1 个练习
Diagnostic Exam16分钟
完成时间为 1 小时
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?
完成时间为 1 小时
3 个视频 （总计 36 分钟）, 1 个阅读材料, 4 个测验
1 个阅读材料
How Grading Works10分钟
4 个练习
Core Homework: Functions16分钟
Challenge Homework: Functions8分钟
Core Homework: The Exponential16分钟
Challenge Homework: The Exponential4分钟
完成时间为 2 小时
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....
完成时间为 2 小时
5 个视频 （总计 69 分钟）
8 个练习
Core Homework: Taylor Series12分钟
Challenge Homework: Taylor Series6分钟
Core Homework: Computing Taylor Series16分钟
Challenge Homework: Computing Taylor Series2分钟
Core Homework: Convergence14分钟
Challenge Homework: Convergence4分钟
Core Homework: Expansion Points10分钟
Challenge Homework: Expansion Points8分钟
完成时间为 3 小时
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.
完成时间为 3 小时
4 个视频 （总计 62 分钟）, 1 个阅读材料, 7 个测验
1 个阅读材料
About the Chapter 1 Exam10分钟
7 个练习
Core Homework: Limits20分钟
Challenge Homework: Limits12分钟
Core Homework: l'Hôpital's Rule12分钟
Challenge Homework: l'Hôpital's Rule10分钟
Core Homework: Orders of Growth20分钟
Challenge Homework: Orders of Growth8分钟
Chapter 1: Functions - Exam20分钟
审阅
4.8
来自CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS的热门评论
由 YG 提供Jul 2, 2018
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.
由 NK 提供Feb 22, 2016
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.
由 RH 提供Dec 15, 2016
Excellent class. Prof. Ghrist has a great teaching style, and his idea to use Taylor Series first is quite effective. Many functions I have shied away from in the past are now familiar to me.
由 NR 提供Jul 10, 2018
It was a great journey with Calculus with the help of Coursera. i learned many things about Functions, Taylor series and Order of Growth. Thank you for creating such a great platfarm for us.
由 KK 提供Jan 26, 2016
This module is fully exhaustive. You will also understand why we need series expansion of a function at a given point and its convergence and other applications. I enjoyed it thoroughly.
由 NL 提供Oct 27, 2016
What can I say? It is so good that I watch the lectures when I have dinner alone. Prof Ghrist absolutely has presented calculus so well that it becomes such an entertainment!
由 SG 提供Nov 29, 2018
Great UI and explanation.Started with the Engg. maths and taking it to high school and for the Developer like me Big O is something which introduced in a appropriate way..:)
由 PR 提供Jun 15, 2018
I easily understood concept that i never understood before. I'd say that this is the perfecto goal of any possible course: make understandable the not-easily-understandab
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.
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