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
Université de PennsylvanieÀ propos de ce cours
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Compétences que vous acquerrez
- Series Expansions
- Calculus
- Series Expansion
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Approx. 14 heures pour terminer
Anglais
Sous-titres : Arabe, Français, Portugais (européen), Chinois (simplifié), Italien, Vietnamien, Allemand, Russe, Anglais, Espagnol
Offert par
Université de Pennsylvanie
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.
Programme de cours : ce que vous apprendrez dans ce cours
1 heure pour terminer
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 heure pour terminer
1 vidéo (Total 8 min), 2 lectures, 1 quiz
3 heures pour terminer
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 heures pour terminer
3 vidéos (Total 36 min), 1 lecture, 4 quiz
5 heures pour terminer
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 heures pour terminer
5 vidéos (Total 69 min)
5 heures pour terminer
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 heures pour terminer
4 vidéos (Total 62 min), 1 lecture, 7 quiz
Avis
- 5 stars80,03 %
- 4 stars15,60 %
- 3 stars2,29 %
- 2 stars0,70 %
- 1 star1,36 %
Meilleurs avis pour CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS
par NL27 oct. 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!
par YX26 juil. 2020
Very good refresh course for calculus. Content could be tough and require a lot of thinking. But I learned a lot or reviewed a lot about the calculus concept in my college year.
par NK22 févr. 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.
par YG2 juil. 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.
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