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.
提供方
Calculus: Single Variable Part 1 - Functions
宾夕法尼亚大学课程信息
149,298 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
100% 在线
立即开始，按照自己的计划学习。
可灵活调整截止日期
根据您的日程表重置截止日期。
完成时间大约为7 小时
英语（English）
字幕：英语（English）, 西班牙语（Spanish）, 中文（简体）
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。
可灵活调整截止日期
根据您的日程表重置截止日期。
完成时间大约为7 小时
英语（English）
字幕：英语（English）, 西班牙语（Spanish）, 中文（简体）
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.
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
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.
常见问题
我什么时候能够访问课程视频和作业？
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
- The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
- The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
完成课程后，我会获得大学学分吗？
此课程不提供大学学分，但部分大学可能会选择接受课程证书作为学分。查看您的合作院校，了解详情。Coursera 上的在线学位和 Mastertrack™ 证书提供获得大学学分的机会。
还有其他问题吗？请访问 学生帮助中心。
