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.
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...
What's included
1 video2 readings2 assignments
Show info about module content
1 video•Total 8 minutes
Introduction•8 minutes
2 readings•Total 20 minutes
Welcome•10 minutes
Your Guide to Getting Started in this Course•10 minutes
2 assignments•Total 60 minutes
Learning Style Preference Survey•30 minutes
Diagnostic Exam•30 minutes
A Review of Functions
Module 2•3 hours to complete
Module details
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?
What's included
3 videos1 reading4 assignments
Show info about module content
3 videos•Total 36 minutes
Functions•16 minutes
Exponentials•15 minutes
BONUS!•5 minutes
1 reading•Total 10 minutes
How Grading Works•10 minutes
4 assignments•Total 120 minutes
Core Homework: Functions•30 minutes
Core Homework: The Exponential•30 minutes
Challenge Homework: Functions•30 minutes
Challenge Homework: The Exponential•30 minutes
Taylor Series
Module 3•5 hours to complete
Module details
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....
What's included
5 videos8 assignments
Show info about module content
5 videos•Total 69 minutes
Taylor Series•15 minutes
Computing Taylor Series•16 minutes
Convergence•16 minutes
BONUS!•7 minutes
Expansion Points•14 minutes
8 assignments•Total 240 minutes
Core Homework: Taylor Series•30 minutes
Core Homework: Computing Taylor Series•30 minutes
Core Homework: Convergence•30 minutes
Core Homework: Expansion Points•30 minutes
Challenge Homework: Taylor Series•30 minutes
Challenge Homework: Computing Taylor Series•30 minutes
Challenge Homework: Convergence•30 minutes
Challenge Homework: Expansion Points•30 minutes
Limits and Asymptotics
Module 4•5 hours to complete
Module details
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.
What's included
4 videos1 reading7 assignments
Show info about module content
4 videos•Total 62 minutes
Limits•15 minutes
l'Hôpital's Rule•17 minutes
Orders of Growth•17 minutes
BONUS!•12 minutes
1 reading•Total 10 minutes
About the Chapter 1 Exam•10 minutes
7 assignments•Total 210 minutes
Core Homework: Limits•30 minutes
Core Homework: l'Hôpital's Rule•30 minutes
Core Homework: Orders of Growth•30 minutes
Chapter 1: Functions - Exam•30 minutes
Challenge Homework: Limits•30 minutes
Challenge Homework: l'Hôpital's Rule•30 minutes
Challenge Homework: Orders of Growth•30 minutes
Instructor
Instructor ratings
Instructor ratings
We asked all learners to give feedback on our instructors based on the quality of their teaching style.
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.
"To be able to take courses at my own pace and rhythm has been an amazing experience. I can learn whenever it fits my schedule and mood."
Jennifer J.
Learner since 2020
"I directly applied the concepts and skills I learned from my courses to an exciting new project at work."
Larry W.
Learner since 2021
"When I need courses on topics that my university doesn't offer, Coursera is one of the best places to go."
Chaitanya A.
"Learning isn't just about being better at your job: it's so much more than that. Coursera allows me to learn without limits."
Learner reviews
4.7
2,389 reviews
5 stars
80.20%
4 stars
14.93%
3 stars
2.51%
2 stars
0.71%
1 star
1.63%
Showing 3 of 2389
V
VP
5·
Reviewed on May 30, 2020
The course is awesome ,I learn lot from this course . Taylor's series and its applications to find limits is very good. Big-O is very useful. Thanks for giving such a wonderful course.
B
BS
5·
Reviewed on Mar 5, 2021
Awesome , I love to do maths ( challenging maths ) like we are playing game and clearing level one by one ,but still it will be better if we get answer of question which we failed to attempt it
Y
YG
5·
Reviewed on Jul 2, 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.
When will I have access to the lectures and assignments?
To access the course materials, assignments and to earn a Certificate, you will need to purchase the Certificate experience when you enroll in a course. You can try a Free Trial instead, or apply for Financial Aid. The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.