About this Course
4.8
805 ratings
211 reviews
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Hours to complete

Approx. 19 hours to complete

Suggested: 6-8 hours/week...
Available languages

English

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

Skills you will gain

Series ExpansionsCalculusSeries Expansion
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Hours to complete

Approx. 19 hours to complete

Suggested: 6-8 hours/week...
Available languages

English

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

Syllabus - What you will learn from this course

Week
1
Hours to complete
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......
Reading
1 video (Total 8 min), 2 readings, 1 quiz
Video1 video
Reading2 readings
Welcome10m
Your Guide to Getting Started in this Course10m
Quiz1 practice exercise
Diagnostic Exam16m
Week
2
Hours to complete
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?...
Reading
3 videos (Total 36 min), 1 reading, 4 quizzes
Video3 videos
Exponentials15m
BONUS!4m
Reading1 reading
How Grading Works10m
Quiz4 practice exercises
Core Homework: Functions16m
Challenge Homework: Functions8m
Core Homework: The Exponential16m
Challenge Homework: The Exponential4m
Week
3
Hours to complete
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.......
Reading
5 videos (Total 69 min), 8 quizzes
Video5 videos
Computing Taylor Series16m
Convergence16m
BONUS!7m
Expansion Points14m
Quiz8 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
Hours to complete
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....
Reading
4 videos (Total 62 min), 1 reading, 7 quizzes
Video4 videos
l'Hôpital's Rule16m
Orders of Growth17m
BONUS!12m
Reading1 reading
About the Chapter 1 Exam10m
Quiz7 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

Instructor

Avatar

Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

About 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. ...

Frequently Asked Questions

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