课程信息
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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. In this first part--part one of five--you will extend your understanding of Taylor series, review limits, learn the *why* behind l'Hopital's rule, and, most importantly, learn a new language for describing growth and decay of functions: the BIG O....
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100% 在线课程

立即开始,按照自己的计划学习。
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Approx. 17 hours to complete

建议:6-8 hours/week...
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字幕:English, Spanish, Chinese (Simplified)...

您将获得的技能

Series ExpansionsCalculusSeries Expansion
Globe

100% 在线课程

立即开始,按照自己的计划学习。
Calendar

可灵活调整截止日期

根据您的日程表重置截止日期。
Clock

Approx. 17 hours to complete

建议:6-8 hours/week...
Comment Dots

English

字幕:English, Spanish, Chinese (Simplified)...

教学大纲 - 您将从这门课程中学到什么

Week
1
Clock
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......
Reading
1 个视频(共 8 分钟), 2 个阅读材料, 1 个测验
Video1 个视频
Reading2 个阅读材料
Welcome10分钟
Your Guide to Getting Started in this Course10分钟
Quiz1 个练习
Diagnostic Exam16分钟
Week
2
Clock
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?...
Reading
3 个视频(共 36 分钟), 1 个阅读材料, 4 个测验
Video3 个视频
Functions15分钟
Exponentials15分钟
BONUS!4分钟
Reading1 个阅读材料
How Grading Works10分钟
Quiz4 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
Week
3
Clock
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.......
Reading
5 个视频(共 69 分钟), 8 个测验
Video5 个视频
Computing Taylor Series16分钟
Convergence16分钟
BONUS!7分钟
Expansion Points14分钟
Quiz8 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
Week
4
Clock
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....
Reading
4 个视频(共 62 分钟), 1 个阅读材料, 7 个测验
Video4 个视频
Limits15分钟
l'Hôpital's Rule16分钟
Orders of Growth17分钟
BONUS!12分钟
Reading1 个阅读材料
About the Chapter 1 Exam10分钟
Quiz7 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

讲师

Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

关于 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. ...

常见问题

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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