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
(2,210 reviews)
14 hours to complete
3 weeks at 4 hours a week
Flexible schedule
Learn at your own pace
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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
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4.7 (448 ratings)
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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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