Calculus: Single Variable

 所在平台: CourseraArchive 课程类别: 数学 授课老师： Robert Ghrist

课程详情

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.

课程大纲

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.

课程评论(4条)

 0 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。
 0 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。
 0 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。
 2 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。

课程简介

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.