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Calculus: Single Variable Part 1 - Functions

Un vistazoProgramaPreguntas FrecuentesCreadores
InicioMatemáticas y Lógica

Calculus: Single Variable Part 1 - Functions

Universidad de Pensilvania

Acerca de este curso: 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. In this first part--part one of five--you will extend your understanding of Taylor series, review limits, learn the *why* behind l'Hopital's rule, and, most importantly, learn a new language for describing growth and decay of functions: the BIG O.


Creada por:  Universidad de Pensilvania
Universidad de Pensilvania

  • Robert Ghrist

    Enseñado por:  Robert Ghrist, Professor

    Mathematics and Electrical & Systems Engineering
Compromiso6-8 hours/week
Idioma
English, Subtítulos: Spanish, Chinese (Simplified)
Cómo aprobarAprueba todas las tareas calificadas para completar el curso.
Programa
SEMANA 1
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 video, 2 readings, 1 practice quiz
  1. Reading: Welcome
  2. Reading: Your Guide to Getting Started in this Course
  3. Vídeo: Introduction
  4. Practice Quiz: Diagnostic Exam
SEMANA 2
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 videos, 1 reading, 2 practice quizzes
  1. Vídeo: Functions
  2. Reading: How Grading Works
  3. Practice Quiz: Challenge Homework: Functions
  4. Vídeo: Exponentials
  5. Vídeo: BONUS!
  6. Practice Quiz: Challenge Homework: The Exponential
Calificado: Core Homework: Functions
Calificado: Core Homework: The Exponential
SEMANA 3
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 videos, 4 practice quizzes
  1. Vídeo: Taylor Series
  2. Practice Quiz: Challenge Homework: Taylor Series
  3. Vídeo: Computing Taylor Series
  4. Practice Quiz: Challenge Homework: Computing Taylor Series
  5. Vídeo: Convergence
  6. Vídeo: BONUS!
  7. Practice Quiz: Challenge Homework: Convergence
  8. Vídeo: Expansion Points
  9. Practice Quiz: Challenge Homework: Expansion Points
Calificado: Core Homework: Taylor Series
Calificado: Core Homework: Computing Taylor Series
Calificado: Core Homework: Convergence
Calificado: Core Homework: Expansion Points
SEMANA 4
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.
4 videos, 1 reading, 3 practice quizzes
  1. Vídeo: Limits
  2. Practice Quiz: Challenge Homework: Limits
  3. Vídeo: l'Hôpital's Rule
  4. Practice Quiz: Challenge Homework: l'Hôpital's Rule
  5. Vídeo: Orders of Growth
  6. Vídeo: BONUS!
  7. Practice Quiz: Challenge Homework: Orders of Growth
  8. Reading: About the Chapter 1 Exam
Calificado: Core Homework: Limits
Calificado: Core Homework: l'Hôpital's Rule
Calificado: Core Homework: Orders of Growth
Calificado: Chapter 1: Functions - Exam

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Creadores
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.
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