4.8
871 ratings
228 reviews

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 19 hours to complete

Suggested: 6-8 hours/week...

#### English

Subtitles: English, Spanish, Chinese (Simplified)

### Skills you will gain

Series ExpansionsCalculusSeries Expansion

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 19 hours to complete

Suggested: 6-8 hours/week...

#### English

Subtitles: English, Spanish, Chinese (Simplified)

### Syllabus - What you will learn from this course

Week
1
1 hour to complete

## 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 video (Total 8 min), 2 readings, 1 quiz
1 video
Welcome10m
Your Guide to Getting Started in this Course10m
1 practice exercise
Diagnostic Exam16m
Week
2
1 hour to complete

## 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 videos (Total 36 min), 1 reading, 4 quizzes
3 videos
Exponentials15m
BONUS!4m
4 practice exercises
Core Homework: Functions16m
Challenge Homework: Functions8m
Core Homework: The Exponential16m
Challenge Homework: The Exponential4m
Week
3
2 hours to complete

## 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 videos (Total 69 min), 8 quizzes
5 videos
Computing Taylor Series16m
Convergence16m
BONUS!7m
Expansion Points14m
8 practice exercises
Core Homework: Taylor Series12m
Challenge Homework: Taylor Series6m
Core Homework: Computing Taylor Series16m
Challenge Homework: Computing Taylor Series2m
Core Homework: Convergence14m
Challenge Homework: Convergence4m
Core Homework: Expansion Points10m
Challenge Homework: Expansion Points8m
Week
4
3 hours to complete

## 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 videos (Total 62 min), 1 reading, 7 quizzes
4 videos
l'Hôpital's Rule16m
Orders of Growth17m
BONUS!12m
7 practice exercises
Core Homework: Limits20m
Challenge Homework: Limits12m
Core Homework: l'Hôpital's Rule12m
Challenge Homework: l'Hôpital's Rule10m
Core Homework: Orders of Growth20m
Challenge Homework: Orders of Growth8m
Chapter 1: Functions - Exam20m
4.8
228 Reviews

## 40%

started a new career after completing these courses

## 37%

got a tangible career benefit from this course

## 18%

got a pay increase or promotion

### Top Reviews

By 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.

By 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.

## Instructor

### Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering