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 PennsylvaniaÜber diesen Kurs
38.038 kürzliche Aufrufe
Flexible Fristen
Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.
100 % online
Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Ca. 14 Stunden zum Abschließen
Englisch
Untertitel: Arabischer Raum, Französisch, Portugiesisch (europäisch), Chinesisch (vereinfacht), Italienisch, Vietnamesisch, Deutsch, Russisch, Englisch, Spanisch
Kompetenzen, die Sie erwerben
- Series Expansions
- Calculus
- Series Expansion
Flexible Fristen
Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.
100 % online
Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Ca. 14 Stunden zum Abschließen
Englisch
Untertitel: Arabischer Raum, Französisch, Portugiesisch (europäisch), Chinesisch (vereinfacht), Italienisch, Vietnamesisch, Deutsch, Russisch, Englisch, Spanisch
von
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.
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
3 Stunden 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?
3 Stunden zum Abschließen
3 Videos (Gesamt 36 min), 1 Lektüre, 4 Quiz
5 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....
5 Stunden zum Abschließen
5 Videos (Gesamt 69 min)
5 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.
5 Stunden zum Abschließen
4 Videos (Gesamt 62 min), 1 Lektüre, 7 Quiz
Bewertungen
- 5 stars80,12 %
- 4 stars15,49 %
- 3 stars2,30 %
- 2 stars0,71 %
- 1 star1,36 %
Top-Bewertungen von CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS
von HB27. Sep. 2020
As a mathematics student in high school who just wanted to learn and explore more in calculus and university math this was a great first step to start with. Can't wait to go for chapter 2!!!
von NL9. Feb. 2021
Excellent introduction to Calculus, I wanted to review the material to tutor my child but I am very happy that I learned a whole new way of looking at Calculus. Thank you so much Prof. Ghrist.
von RH15. Dez. 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 AT13. Aug. 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.
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