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完成時間大約為20 小時

建議:6-8 hours/week...

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字幕:英語(English), 西班牙語(Spanish), 中文(簡體)

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Series ExpansionsCalculusSeries Expansion

100% 在線

立即開始,按照自己的計劃學習。

可靈活調整截止日期

根據您的日程表重置截止日期。

完成時間大約為20 小時

建議:6-8 hours/week...

英語(English)

字幕:英語(English), 西班牙語(Spanish), 中文(簡體)

教學大綱 - 您將從這門課程中學到什麼

1
完成時間為 1 小時

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 個視頻 (總計 8 分鐘), 2 個閱讀材料, 1 個測驗
1 個視頻
2 個閱讀材料
Welcome10分鐘
Your Guide to Getting Started in this Course10分鐘
1 個練習
Diagnostic Exam16分鐘
2
完成時間為 1 小時

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 個視頻 (總計 36 分鐘), 1 個閱讀材料, 4 個測驗
3 個視頻
Functions15分鐘
Exponentials15分鐘
BONUS!4分鐘
1 個閱讀材料
How Grading Works10分鐘
4 個練習
Core Homework: Functions16分鐘
Challenge Homework: Functions8分鐘
Core Homework: The Exponential16分鐘
Challenge Homework: The Exponential4分鐘
3
完成時間為 2 小時

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 個視頻 (總計 69 分鐘), 8 個測驗
5 個視頻
Computing Taylor Series16分鐘
Convergence16分鐘
BONUS!7分鐘
Expansion Points14分鐘
8 個練習
Core Homework: Taylor Series12分鐘
Challenge Homework: Taylor Series6分鐘
Core Homework: Computing Taylor Series16分鐘
Challenge Homework: Computing Taylor Series2分鐘
Core Homework: Convergence14分鐘
Challenge Homework: Convergence4分鐘
Core Homework: Expansion Points10分鐘
Challenge Homework: Expansion Points8分鐘
4
完成時間為 3 小時

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....
4 個視頻 (總計 62 分鐘), 1 個閱讀材料, 7 個測驗
4 個視頻
Limits15分鐘
l'Hôpital's Rule16分鐘
Orders of Growth17分鐘
BONUS!12分鐘
1 個閱讀材料
About the Chapter 1 Exam10分鐘
7 個練習
Core Homework: Limits20分鐘
Challenge Homework: Limits12分鐘
Core Homework: l'Hôpital's Rule12分鐘
Challenge Homework: l'Hôpital's Rule10分鐘
Core Homework: Orders of Growth20分鐘
Challenge Homework: Orders of Growth8分鐘
Chapter 1: Functions - Exam20分鐘
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創建者 YGJul 3rd 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.

創建者 RHDec 16th 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.

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Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

關於 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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