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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Résultats de carrière des étudiants
33%
ont commencé une nouvelle carrière après avoir terminé ce cours
28%
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13%
a obtenu une augmentation de salaire ou une promotion
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Approx. 14 heures pour terminer
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Sous-titres : Arabe, Français, Portugais (européen), Chinois (simplifié), Italien, Vietnamien, Coréen, Allemand, Russe, Turc, Anglais, Espagnol
Compétences que vous acquerrez
Series ExpansionsCalculusSeries Expansion
Résultats de carrière des étudiants
33%
ont commencé une nouvelle carrière après avoir terminé ce cours
28%
ont bénéficié d'un avantage concret dans leur carrières grâce à ce cours
13%
a obtenu une augmentation de salaire ou une promotion
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
Approx. 14 heures pour terminer
Anglais
Sous-titres : Arabe, Français, Portugais (européen), Chinois (simplifié), Italien, Vietnamien, Coréen, Allemand, Russe, Turc, 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 du 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
1 vidéo
Introduction8 min
2 lectures
Welcome10 min
Your Guide to Getting Started in this Course10 min
1 exercice pour s'entraîner
Diagnostic Exam30 min
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
1 lecture
How Grading Works10 min
4 exercices pour s'entraîner
Core Homework: Functions30 min
Challenge Homework: Functions30 min
Core Homework: The Exponential30 min
Challenge Homework: The Exponential30 min
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 vidéos
Taylor Series14 min
Computing Taylor Series16 min
Convergence16 min
BONUS!7 min
Expansion Points14 min
8 exercices pour s'entraîner
Core Homework: Taylor Series30 min
Challenge Homework: Taylor Series30 min
Core Homework: Computing Taylor Series30 min
Challenge Homework: Computing Taylor Series30 min
Core Homework: Convergence30 min
Challenge Homework: Convergence30 min
Core Homework: Expansion Points30 min
Challenge Homework: Expansion Points30 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
1 lecture
About the Chapter 1 Exam10 min
7 exercices pour s'entraîner
Core Homework: Limits30 min
Challenge Homework: Limits30 min
Core Homework: l'Hôpital's Rule30 min
Challenge Homework: l'Hôpital's Rule30 min
Core Homework: Orders of Growth30 min
Challenge Homework: Orders of Growth30 min
Chapter 1: Functions - Exam30 min
Avis
Meilleurs avis pour CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS
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.
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 KR17 août 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.
par RH15 déc. 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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