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.
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Calculus: Single Variable Part 1 - Functions
University of Pennsylvania
Über diesen Kurs
174,335 kürzliche Aufrufe
Karriereergebnisse der Lernenden
35%
nahm einen neuen Beruf nach Abschluss dieser Kurse auf
30%
ziehen Sie für Ihren Beruf greifbaren Nutzen aus diesem Kurs
15%
erhalten Sie eine Gehaltserhöhung oder Beförderung
Kompetenzen, die Sie erwerben
Series ExpansionsCalculusSeries Expansion
Karriereergebnisse der Lernenden
35%
nahm einen neuen Beruf nach Abschluss dieser Kurse auf
30%
ziehen Sie für Ihren Beruf greifbaren Nutzen aus diesem Kurs
15%
erhalten Sie eine Gehaltserhöhung oder Beförderung
100 % online
Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Flexible Fristen
Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.
Ca. 21 Stunden zum Abschließen
Empfohlen: 6-8 hours/week
Englisch
Untertitel: Englisch, Spanisch, Chinesisch (vereinfacht)
Lehrplan - Was Sie in diesem Kurs lernen werden
1 Stunde zum Abschließen
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 Stunde zum Abschließen
1 Video (Gesamt 8 min), 2 Lektüren, 1 Quiz
1 Video
2 Lektüren
Welcome10m
Your Guide to Getting Started in this Course10m
1 praktische Übung
Diagnostic Exam16m
1 Stunde zum Abschließen
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?
1 Stunde zum Abschließen
3 Videos (Gesamt 36 min), 1 Lektüre, 4 Quiz
1 Lektüre
How Grading Works10m
4 praktische Übungen
Core Homework: Functions16m
Challenge Homework: Functions8m
Core Homework: The Exponential16m
Challenge Homework: The Exponential4m
2 Stunden zum Abschließen
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....
2 Stunden zum Abschließen
5 Videos (Gesamt 69 min)
8 praktische Übungen
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
3 Stunden zum Abschließen
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.
3 Stunden zum Abschließen
4 Videos (Gesamt 62 min), 1 Lektüre, 7 Quiz
1 Lektüre
About the Chapter 1 Exam10m
7 praktische Übungen
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
Bewertungen
Top-Bewertungen von CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS
von 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.
von 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.
von 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.
von NRJul 10, 2018
It was a great journey with Calculus with the help of Coursera. i learned many things about Functions, Taylor series and Order of Growth. Thank you for creating such a great platfarm for us.
von KKJan 26, 2016
This module is fully exhaustive. You will also understand why we need series expansion of a function at a given point and its convergence and other applications. I enjoyed it thoroughly.
von NLOct 27, 2016
What can I say? It is so good that I watch the lectures when I have dinner alone. Prof Ghrist absolutely has presented calculus so well that it becomes such an entertainment!
von SGNov 29, 2018
Great UI and explanation.Started with the Engg. maths and taking it to high school and for the Developer like me Big O is something which introduced in a appropriate way..:)
von PRJun 15, 2018
I easily understood concept that i never understood before. I'd say that this is the perfecto goal of any possible course: make understandable the not-easily-understandab
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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.
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