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.
Offered By
Calculus: Single Variable Part 1 - Functions
University of PennsylvaniaAbout this Course
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Learner Career Outcomes
33%
started a new career after completing these courses
28%
got a tangible career benefit from this course
13%
got a pay increase or promotion
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Start instantly and learn at your own schedule.
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Approx. 14 hours to complete
English
Subtitles: Arabic, French, Portuguese (Brazilian), Chinese (Simplified), Italian, Vietnamese, Korean, German, Russian, Turkish, English, Spanish, Chinese
Skills you will gain
Series ExpansionsCalculusSeries Expansion
Learner Career Outcomes
33%
started a new career after completing these courses
28%
got a tangible career benefit from this course
13%
got a pay increase or promotion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Approx. 14 hours to complete
English
Subtitles: Arabic, French, Portuguese (Brazilian), Chinese (Simplified), Italian, Vietnamese, Korean, German, Russian, Turkish, English, Spanish, Chinese
Offered by
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.
Syllabus - What you will learn from this course
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 hour to complete
1 video (Total 8 min), 2 readings, 1 quiz
1 video
2 readings
Welcome10m
Your Guide to Getting Started in this Course10m
1 practice exercise
Diagnostic Exam30m
3 hours 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 hours to complete
3 videos (Total 36 min), 1 reading, 4 quizzes
1 reading
How Grading Works10m
4 practice exercises
Core Homework: Functions30m
Challenge Homework: Functions30m
Core Homework: The Exponential30m
Challenge Homework: The Exponential30m
5 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 hours to complete
5 videos (Total 69 min)
8 practice exercises
Core Homework: Taylor Series30m
Challenge Homework: Taylor Series30m
Core Homework: Computing Taylor Series30m
Challenge Homework: Computing Taylor Series30m
Core Homework: Convergence30m
Challenge Homework: Convergence30m
Core Homework: Expansion Points30m
Challenge Homework: Expansion Points30m
5 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.
5 hours to complete
4 videos (Total 62 min), 1 reading, 7 quizzes
1 reading
About the Chapter 1 Exam10m
7 practice exercises
Core Homework: Limits30m
Challenge Homework: Limits30m
Core Homework: l'Hôpital's Rule30m
Challenge Homework: l'Hôpital's Rule30m
Core Homework: Orders of Growth30m
Challenge Homework: Orders of Growth30m
Chapter 1: Functions - Exam30m
Reviews
TOP REVIEWS FROM CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS
by YGJul 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.
by NKFeb 22, 2016
Would have preferred accompanying solutions. Just getting the answer ain't enough. Making sure my approach is correct is essential as well considering the course touches upon the absolute basics.
by KRAug 17, 2020
Very good and challenging material! This motivated me to do better in my Calculus Courses. Would definitely have more of these courses soon, as this is suited for higher mathematics in college.
by RHDec 15, 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.
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