Calculus: Single Variable Part 1 - Functions

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Opleiderscore: starstarstarstar_borderstar_border 6,3 Coursera heeft een gemiddelde beoordeling van 6,3 (uit 4 ervaringen)

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Beschrijving

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About this course: 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, un…

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Heb je een vraag? Onze adviseurs helpen je graag. Bel ons op 085 7440830 of e-mail naar info@springest.nl.

When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

About this course: 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.

Created by:  University of Pennsylvania
  • Taught by:  Robert Ghrist, Professor

    Mathematics and Electrical & Systems Engineering
Commitment 6-8 hours/week Language English, Subtitles: Spanish, Chinese (Simplified) How To Pass Pass all graded assignments to complete the course. Coursework

Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.

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University of Pennsylvania 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.

Syllabus


WEEK 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 expand


  1. Reading: Welcome
  2. Reading: Your Guide to Getting Started in this Course
  3. Video: Introduction
  4. Practice Quiz: Diagnostic Exam


WEEK 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 expand


  1. Video: Functions
  2. Reading: How Grading Works
  3. Practice Quiz: Challenge Homework: Functions
  4. Video: Exponentials
  5. Video: BONUS!
  6. Practice Quiz: Challenge Homework: The Exponential

Graded: Core Homework: Functions
Graded: Core Homework: The Exponential

WEEK 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 expand


  1. Video: Taylor Series
  2. Practice Quiz: Challenge Homework: Taylor Series
  3. Video: Computing Taylor Series
  4. Practice Quiz: Challenge Homework: Computing Taylor Series
  5. Video: Convergence
  6. Video: BONUS!
  7. Practice Quiz: Challenge Homework: Convergence
  8. Video: Expansion Points
  9. Practice Quiz: Challenge Homework: Expansion Points

Graded: Core Homework: Taylor Series
Graded: Core Homework: Computing Taylor Series
Graded: Core Homework: Convergence
Graded: Core Homework: Expansion Points

WEEK 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 expand


  1. Video: Limits
  2. Practice Quiz: Challenge Homework: Limits
  3. Video: l'Hôpital's Rule
  4. Practice Quiz: Challenge Homework: l'Hôpital's Rule
  5. Video: Orders of Growth
  6. Video: BONUS!
  7. Practice Quiz: Challenge Homework: Orders of Growth
  8. Reading: About the Chapter 1 Exam

Graded: Core Homework: Limits
Graded: Core Homework: l'Hôpital's Rule
Graded: Core Homework: Orders of Growth
Graded: Chapter 1: Functions - Exam

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