此课程(MOOCULUS-2 "Sequences and Series")由Ohio State University于2014年在Coursera平台讲授. PDF格式教材下载 Sequences and Series 本系列学习笔记PDF下载(Academia.edu) MOOCULUS-2 Solution Summary Given a function $f$, the series $$\sum_{n=0}^\infty {f^{(n)}(0)\over n!}x^n$$…
w用有限来表达无限,由已知到未知,化未知为已知. https://en.wikipedia.org/wiki/Taylor_series The Greek philosopher Zeno considered the problem of summing an infinite series to achieve a finite result, but rejected it as an impossibility: the result was Zeno's paradox. Later…
此课程(MOOCULUS-2 "Sequences and Series")由Ohio State University于2014年在Coursera平台讲授. PDF格式教材下载 Sequences and Series 本系列学习笔记PDF下载(Academia.edu) MOOCULUS-2 Solution Summary Let $(a_n)$ be a sequence of real numbers starting with $a_0$. Then the power…
2ed, by Timothy Sauer DEFINITION 1.3A solution is correct within p decimal places if the error is less than 0.5 × 10$^{−p}$ .-P29Bisection Method的优点是计算次数(step)是确定的(interval<精度).后面介绍的算法的interval是不确定的, 所以什么时候结束计算呢?不知道.所以定义“stopping criteria’’来决定什么时候结束…
Define on \(\mathbb{R}^d\) the normalized Gaussian measure\[ d \gamma(x)=\frac{1}{(2\pi)^{\frac{d}{2}}} e^{-\frac{|x|^2}{2}}dx\] Consider first the case \(d= 1\). The Taylor expansion of \(e^{-\frac{1}{2}x^2}\) at the point \(x\), with increment \(t\…
此课程(MOOCULUS-2 "Sequences and Series")由Ohio State University于2014年在Coursera平台讲授. PDF格式教材下载 Sequences and Series 本系列学习笔记PDF下载(Academia.edu) MOOCULUS-2 Solution Review Determine whether the series converges. 1. $\displaystyle\sum_{n=0}^{\infty}{n\…
