Calculus: Single Variable Part 1 - Functions
提供方
Calculus: Single Variable Part 1 - Functions
University of Pennsylvania
课程信息
4.8
791 个评分
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.
您将获得的技能
Series ExpansionsCalculusSeries Expansion
教学大纲 - 您将从这门课程中学到什么
Week
1Introduction
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 个视频（共 8 分钟）, 2 个阅读材料, 1 个测验
1 个视频
Introduction8分钟
2 个阅读材料
Welcome10分钟
Your Guide to Getting Started in this Course10分钟
1 个练习
Diagnostic Exam16分钟
Week
2A 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 个视频（共 36 分钟）, 1 个阅读材料, 4 个测验
1 个阅读材料
How Grading Works10分钟
4 个练习
Core Homework: Functions16分钟
Challenge Homework: Functions8分钟
Core Homework: The Exponential16分钟
Challenge Homework: The Exponential4分钟
Week
3Taylor 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 个视频（共 69 分钟）, 8 个测验
8 个练习
Core Homework: Taylor Series12分钟
Challenge Homework: Taylor Series6分钟
Core Homework: Computing Taylor Series16分钟
Challenge Homework: Computing Taylor Series2分钟
Core Homework: Convergence14分钟
Challenge Homework: Convergence4分钟
Core Homework: Expansion Points10分钟
Challenge Homework: Expansion Points8分钟
Week
4Limits 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 个视频（共 62 分钟）, 1 个阅读材料, 7 个测验
1 个阅读材料
About the Chapter 1 Exam10分钟
7 个练习
Core Homework: Limits20分钟
Challenge Homework: Limits12分钟
Core Homework: l'Hôpital's Rule12分钟
Challenge Homework: l'Hôpital's Rule10分钟
Core Homework: Orders of Growth20分钟
Challenge Homework: Orders of Growth8分钟
Chapter 1: Functions - Exam20分钟
讲师
Robert Ghrist
ProfessorMathematics and Electrical & Systems Engineering
关于 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.
常见问题
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