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.
Calculus: Single Variable Part 1 - Functions
Gain insight into a topic and learn the fundamentals.
4.7
(2,233 reviews)
14 hours to complete
3 weeks at 4 hours a week
Flexible schedule
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Assessments
21 assignments
Taught in English
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There are 4 modules in this course
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
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
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
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
Instructor
Instructor ratings
4.7 (459 ratings)
Offered by
Recommended if you're interested in Math and Logic
University of Pennsylvania
University of Pennsylvania
University of Pennsylvania
University of Pennsylvania
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4.7
2,233 reviews
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Showing 3 of 2233
JV
5
Reviewed on Jun 1, 2020
Very Informative course and easy to catch. Although knowledge on the subject is a prerequisite before taking this. Not advisable to those with no knowledge whatsoever in calculus.
AT
4
Reviewed on Aug 13, 2020
Very insightful. However, I believe (although I may be wrong) that certain methods and techniques required to solve the homework problems weren't explained in the course material.
YF
4
Reviewed on Sep 19, 2020
There were certain advanced concepts that could have had a better and clearer explanation such as the “big O”. But on the whole it was a very good course and very much recommendable.
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