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Series ExpansionsCalculusSeries Expansion

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Prazos flexíveis

Redefinir os prazos de acordo com sua programação.

Aprox. 20 horas para completar

Sugerido: 6-8 hours/week...

Inglês

Legendas: Inglês, Espanhol, Chinês (simplificado)

Programa - O que você aprenderá com este curso

Semana
1
1 hora para concluir

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...

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1 vídeo ((Total 8 mín.)), 2 leituras, 1 teste
1 vídeos
2 leituras
Welcome10min
Your Guide to Getting Started in this Course10min
1 exercício prático
Diagnostic Exam16min
Semana
2
1 hora para concluir

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?

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3 vídeos ((Total 36 mín.)), 1 leitura, 4 testes
3 videos
Exponentials15min
BONUS!4min
1 leituras
How Grading Works10min
4 exercícios práticos
Core Homework: Functions16min
Challenge Homework: Functions8min
Core Homework: The Exponential16min
Challenge Homework: The Exponential4min
Semana
3
2 horas para concluir

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....

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5 vídeos ((Total 69 mín.)), 8 testes
5 videos
Computing Taylor Series16min
Convergence16min
BONUS!7min
Expansion Points14min
8 exercícios práticos
Core Homework: Taylor Series12min
Challenge Homework: Taylor Series6min
Core Homework: Computing Taylor Series16min
Challenge Homework: Computing Taylor Series2min
Core Homework: Convergence14min
Challenge Homework: Convergence4min
Core Homework: Expansion Points10min
Challenge Homework: Expansion Points8min
Semana
4
3 horas para concluir

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.

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4 vídeos ((Total 62 mín.)), 1 leitura, 7 testes
4 videos
Limits15min
l'Hôpital's Rule16min
Orders of Growth17min
BONUS!12min
1 leituras
About the Chapter 1 Exam10min
7 exercícios práticos
Core Homework: Limits20min
Challenge Homework: Limits12min
Core Homework: l'Hôpital's Rule12min
Challenge Homework: l'Hôpital's Rule10min
Core Homework: Orders of Growth20min
Challenge Homework: Orders of Growth8min
Chapter 1: Functions - Exam20min
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Principais avaliações do Calculus: Single Variable Part 1 - Functions

por 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.

por 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.

Instrutores

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Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

Sobre Universidade da Pensilvânia

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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