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.
ofrecido por
Calculus: Single Variable Part 1 - Functions
Universidad de Pensilvania
Acerca de este Curso
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Resultados profesionales del estudiante
35%
comenzó una nueva carrera después de completar estos cursos
30%
consiguió un beneficio tangible en su carrera profesional gracias a este curso
15%
consiguió un aumento de sueldo o ascenso
Habilidades que obtendrás
Series ExpansionsCalculusSeries Expansion
Resultados profesionales del estudiante
35%
comenzó una nueva carrera después de completar estos cursos
30%
consiguió un beneficio tangible en su carrera profesional gracias a este curso
15%
consiguió un aumento de sueldo o ascenso
100 % en línea
Comienza de inmediato y aprende a tu propio ritmo.
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Aprox. 23 horas para completar
Inglés (English)
Subtítulos: Inglés (English), Español (Spanish), Chino (simplificado)
ofrecido por
Universidad de Pensilvania
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 - Qué aprenderás en este curso
1 hora para completar
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 completar
1 video (Total 8 minutos), 2 lecturas, 1 cuestionario
1 video
2 lecturas
Welcome10m
Your Guide to Getting Started in this Course10m
1 ejercicio de práctica
Diagnostic Exam16m
1 hora para completar
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 completar
3 videos (Total 36 minutos), 1 lectura, 4 cuestionarios
1 lectura
How Grading Works10m
4 ejercicios de práctica
Core Homework: Functions16m
Challenge Homework: Functions8m
Core Homework: The Exponential16m
Challenge Homework: The Exponential4m
2 horas para completar
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 completar
5 videos (Total 69 minutos)
8 ejercicios de práctica
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 horas para completar
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 completar
4 videos (Total 62 minutos), 1 lectura, 7 cuestionarios
1 lectura
About the Chapter 1 Exam10m
7 ejercicios de práctica
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
Revisiones
Principales revisiones sobre 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.
Preguntas Frecuentes
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