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.
oferecido por
Calculus: Single Variable Part 1 - Functions
Universidade da Pensilvânia
Informações sobre o curso
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Resultados de carreira do aprendiz
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consegui um benefício significativo de carreira com este curso
15%
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Habilidades que você terá
Series ExpansionsCalculusSeries Expansion
Resultados de carreira do aprendiz
35%
comecei uma nova carreira após concluir estes cursos
30%
consegui um benefício significativo de carreira com este curso
15%
recebi um aumento ou promoção
100% on-line
Comece imediatamente e aprenda em seu próprio cronograma.
Prazos flexíveis
Redefinir os prazos de acordo com sua programação.
Aprox. 21 horas para completar
Sugerido: 6-8 hours/week
Inglês
Legendas: Inglês, Espanhol, Chinês (simplificado)
oferecido por
Universidade da Pensilvânia
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.
Programa - O que você aprenderá com este curso
1 hora para concluir
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 hora para concluir
1 vídeo (Total 8 mín.), 2 leituras, 1 teste
1 vídeos
Introduction8min
2 leituras
Welcome10min
Your Guide to Getting Started in this Course10min
1 exercício prático
Diagnostic Exam16min
1 hora para concluir
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 hora para concluir
3 vídeos (Total 36 mín.), 1 leitura, 4 testes
1 leituras
How Grading Works10min
4 exercícios práticos
Core Homework: Functions16min
Challenge Homework: Functions8min
Core Homework: The Exponential16min
Challenge Homework: The Exponential4min
2 horas para concluir
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 horas para concluir
5 vídeos (Total 69 mín.)
5 videos
Taylor Series14min
Computing Taylor Series16min
Convergence16min
BONUS!7min
Expansion Points14min
8 exercícios práticos
Core Homework: Taylor Series12min
Challenge Homework: Taylor Series6min
Core Homework: Computing Taylor Series16min
Challenge Homework: Computing Taylor Series2min
Core Homework: Convergence14min
Challenge Homework: Convergence4min
Core Homework: Expansion Points10min
Challenge Homework: Expansion Points8min
3 horas para concluir
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 horas para concluir
4 vídeos (Total 62 mín.), 1 leitura, 7 testes
1 leituras
About the Chapter 1 Exam10min
7 exercícios práticos
Core Homework: Limits20min
Challenge Homework: Limits12min
Core Homework: l'Hôpital's Rule12min
Challenge Homework: l'Hôpital's Rule10min
Core Homework: Orders of Growth20min
Challenge Homework: Orders of Growth8min
Chapter 1: Functions - Exam20min
Avaliações
Principais avaliações do CALCULUS: SINGLE VARIABLE PART 1 - FUNCTIONS
por 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.
por 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.
por 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.
por 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.
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