Calculus Two: Sequences and Series

开始时间: 03/01/2014 持续时间: 6 weeks

所在平台: Coursera

课程类别: 数学

大学或机构: The Ohio State University(美国俄亥俄州立大学)

授课老师: Jim Fowler

   

课程主页: https://www.coursera.org/course/sequence

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课程详情

Sequences and Series will challenge us to think very carefully about
"infinity."  What does it mean to add up an unending list of numbers?
How can an infinite task result in a finite answer?  These questions
lead us to some very deep concepts—but also to some powerful
computational tools which are used not only in math but in many
quantitative disciplines.

This course is a first and friendly introduction to sequences, infinite
series, convergence tests, and Taylor series.  It is suitable for
someone who has seen just a bit of calculus before.  And since one
learns mathematics by doing mathematics, this course encourages you to
participate by providing plenty of computational problems, conceptual
projects, and opportunities to explain your thought process to your
peers.

课程大纲

Week 1: Sequences
Week 2: Series
Week 3: Convergence tests
Week 4: Alternating series
Week 5: Power series
Week 6: Taylor series

课程评论(1条)

0

基佬的愛__ 2013-11-27 11:27 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.

这门课讲数列和级数,相同的内容 Robert Ghrist 的 Calculus: Single Variable 也涉及到了。Jim 讲的要比 Robert 要细致,比如一些数列和级数的收敛性的测试定理,Jim 会花一整个 lecture 讲推导过程, Robert 讲的没那么详细。另外整门课我最喜欢的一个 lecture 是关于 Taylor series 那节,Taylor Series 的 motivation 就是 approximation ,实际上他是 linear approximation 的推广,对某个函数在某点做 Taylor expansion 实现上就是找一个函数,使他在该点的值和原函数相等,并且该点的每一阶导数也和原函数的每一阶导数相等,导数反映的是函数的变化情况,这样我们就找到了一个和原函数在某个区间内相同的函数,说在某个区间内是因为有一个收敛性的问题。我可能记不住 Taylor series 的公式,不过我已经随时能把 Taylor series 推导出来了。还有个很有意思的 lecture,为了说明 geometric series 的收敛性,Jim 举了个造桥的问题,用质量均匀分布、形状相同的长木条造桥,最多能造多远?答案是理想状况下,想多远就多远。只要我们把每一块木条放在下一堆木条的重心处就能保证它不倒,然后你会发现每次增加的长度加起来正好构成一个不收敛的级数,Jim 自己造了这么一座很壮观的桥,你能看到这门课课程介绍的图片就是这样一座桥,实际上 lecture 里 Jim 造的那座还要壮观,比课程介绍里的那座要更长。总体来说这门课内容不多、难度不大、(不过我之前已经上过 Robert 的课,并且自学过一些其他的数学)、占用的时间不多,我基本看完视频就马上能把作业完成,不过这门课还是很有启发性的,有很多有意思的东西,Jim 在课程讨论版里也是一如既往的 supportive。另外这门课也有一本配套的免费教材。

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课程简介

Calculus Two: Sequences and Series is an introduction to sequences, infinite series, convergence tests, and Taylor series. The course emphasizes not just getting answers, but asking the question "why is this true?"

课程标签

微积分 微积分二 数列 级数 无穷级数 泰勒级数 俄亥俄州立大学

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