Calculus: Single Variable

开始时间: 04/22/2022 持续时间: Unknown

所在平台: CourseraArchive

课程类别: 数学

大学或机构: University of Pennsylvania(宾夕法尼亚大学)

授课老师: Robert Ghrist


课程评论: 4 个评论

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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:

  • the introduction and use of Taylor series and approximations from the beginning;
  • a novel synthesis of discrete and continuous forms of Calculus;
  • an emphasis on the conceptual over the computational; and
  • a clear, entertaining, unified approach.


The course is divided into five "chapters":

CHAPTER 1: Functions
After a brief review of the basics, we will dive into Taylor series as a way of working with and approximating complicated functions. The chapter will use a series-based approach to understanding limits and asymptotics.

CHAPTER 2: Differentiation
Though you already know how to differentiate some functions, you may not know what differentiation means. This chapter will emphasize conceptual understanding and applications of derivatives.

CHAPTER 3: Integration
We will use the indefinite integral (an anti-derivative) as a motivation to look at differential equations in applications ranging from population models to linguistics to coupled oscillators. Techniques of integration up to and including computer-assisted methods will lead to Riemann sums and the definite integral.

CHAPTER 4: Applications
We will get busy in this chapter with applications of the definite integral to problems in geometry, physics, economics, biology, probability, and more. You will learn how to solve a wide array of problems using a consistent conceptual approach.

CHAPTER 5: Discretization
Having covered Calculus for functions with a single real input and a single real output, we turn to functions with a discrete input and a real output: sequences. We will re-develop all of Calculus (limits, derivatives, integrals, differential equations) in this new context, and return to the beginning of the course with a deeper consideration of Taylor series.

A more detailed lecture-by-lecture syllabus can be found here.



基佬的愛__ 2013-11-27 12:10 0 票支持; 0 票反对

Disclaimer: the review is more or less subjective. I have absolutely no intention to make it objective. You have been informed.

Robert Ghrist 这门课和 Jim Fowler 的 Calculus One 有重叠的部分,不过内容更深入,课程周期也挺长的。课程总共分五个部分,Functions,Differentiation,Integration,Applications(主要是积分的),Discretization(主要讲数列和级数)。积分的应用部分略有难度,讲的内容比我以前上的高数课讲的积分的应用要多 centroids 和 moments and gyrations 我是第一次学,第一部分的 Taylor series 我觉得没有 Jim Fowler 讲的好。这门课作业量挺大的,每周大概是五个 lecture(外加一亮个 bonus),每个 lecture 对应一个 core 和 一个 challenge 作业,core 一般10道左右,challenge 一般2-5道左右,我做了所有的 core 和一部分的 challenge 。作业是不计分的,某个单元会有一次 quiz,期末会有个 exam。另外,讲师是个 geek,他的 lecture 里很多彩蛋。


课程图谱 2013-06-01 12:03 0 票支持; 0 票反对

今天开始跟这门课,写一些我所了解的信息。首先课程的章节比较少,只有5章,但是周期比较长,13周;第二,课程最终的分数是平时每章测试占4%,总计20%,最终考试占80%,不过切勿不做平时的测验和作业,一旦错过结束时间,貌似证书也拿不到了;第三,在这门课的欢迎词里,写了一句话:you're about to begin the largest and most colorful Calculus course in the world. 最后欢迎感兴趣的朋友加入这门课程,大家一起学习体验。


52nlp 2013-05-20 12:43 0 票支持; 0 票反对

Coursera在今年一月份同时推出了两门微积分课程,一门是这个单变量微积分,另一个是微积分上(Calculus One)。我同时跟了这两门课,不过由于工作及春节等等缘故,大概跟了一半就放弃了,不过还是可以点评一下。相对来说,这门课制作的课件非常有意思,但是Calculus One讲得更生动一些。

这门课程的一个参考书是不到50页的一个小册子:FLCT: the Funny Little Calculus Text ,这个在google book上能阅读免费电子版,google play 上也只有0.45美元的价格,课件的确很有趣并且动感实足,这样导致感觉老师讲得有点不生动了。不过总体来说,这门微积分入门课还是非常不错的。


课程图谱 2013-05-12 11:42 2 票支持; 0 票反对

Hello, World! 我是来打酱油的。


This course provides a brisk, entertaining treatment of differential and integral calculus, with an emphasis on conceptual understanding and applications to the engineering, physical, and social sciences.


数学 微积分 单变量微积分 微积分学习 微积分入门 宾夕法尼亚大学



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