此文是对 [Introduction to Differential Equations,Michael E.Taylor] 第3页的一个注记.在该页中,作者给了微分方程$$\frac{dx}{dt}=x,x(0)=1.$$一个幂级数的解法.设$$x(t)=a_0t^0+a_1t^1+a_2t^2+a_3t^3+a_4t^4+\cdots$$注意,作者这样设之后,其实已经假定存在一个实解析函数满足该微分方程,剩下的就是解出该实解析函数.为此,作者进行逐项微分.$$x'(t)=a_1+2a_2t+…

As noted,if $z=x+iy$,$x,y\in\mathbf{R}$,then $|z|=\sqrt{x^2+y^2}$ is equivalent to $|z|^2=z\overline{z}$.Use this to show that if also $w\in\mathbf{C}$,$$|zw|=|z|\cdot|w|.$$ Solve:  $|zw|^{2}=(zw)\cdot  (\overline{zw})=(zw)\cdot(\overline{z}\cdot\ove…

1.Introduction 2.First-order Differential Equations Exercise2.1. Find solutons of the following intial-value problems in $\bbR^2$: (1)$2u_y-u_x+xu=0$ with $u(x,0)=2xe^{x^2/2}$; (2)$u_y+(1+x^2)u_x-u=0$ with $u(x,0)=\arctan x$. Solution: (1)Since $(-1,…

A Basic Course in Partial Differential Equations, Qing Han, 2011 [下载说明:点击链接,等待5秒, 点击右上角的跳过广告后调至下载页面, 点击电信下载即可] http://adf.ly/dNpi7           http://adf.ly/dNplx 习题解答请见:http://bbs.sciencenet.cn/thread-1337491-1-1.html 或者在线观看: http://www.cnblogs.com/zh…

title: [线性代数]6-3:微分方程的应用(Applications to Differential Equations) categories: Mathematic Linear Algebra keywords: Eigenvalues Eigenvectors Differential Equations toc: true date: 2017-11-22 15:09:04 Abstract: 本文主要介绍线性代数在微分方程中的应用 Keywords: Eigenvalues,E…

NIPS2018最佳论文解读:Neural Ordinary Differential Equations 雷锋网2019-01-10 23:32     雷锋网 AI 科技评论按,不久前,NeurIPS 2018 在加拿大蒙特利尔召开,在这次著名会议上获得最佳论文奖之一的论文是<Neural Ordinary Differential Equations>,论文地址:https://arxiv.org/abs/1806.07366.Branislav Holländer 在 towards…

tex文档: \documentclass[a4paper, 12pt]{article} % Font size (can be 10pt, 11pt or 12pt) and paper size (remove a4paper for US letter paper) \usepackage{amsmath,amsfonts,bm} \usepackage{hyperref} \usepackage{amsthm,epigraph} \usepackage{amssymb} \usepac…

原文链接:An Introduction to Differential Privacy 差分隐私算法可以允许分析人员执行良性的聚合分析,同时保证个人隐私得到切实的保护.. 背景数据分析中的隐私保护技术已有数十年的历史,差分隐私算法是这一领域的最新技术.两个早期概念直接影响了差分隐私:①最小查询集大小②Dalenius的统计披露定义 最小查询集大小旨在确保聚合查询的安全性,最小查询集大小是一种约束,只在确保聚合查询不会泄露有关个人的信息,给定某个配置的阈值量T,其确保每个聚合查询在至少有T个记录…

Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. Before: a discrete sequence of hidden layers. After: the derivative of the hidden state. Traditional methods: resid…

(Newton 1671, “Problema II, Solutio particulare”). Solve the total differential equation $$3x^2-2ax+ay-3y^2y'+axy'=0.$$Solve:We have $$y'(3y^2-ax)=3x^2-2ax+ay.$$So$$dy(3y^2-ax)=(3x^2-2ax+ay)dx.$$So $$y^{3}-axy=x^3-ax^2+axy+C$$where $c$ is a constant.…

Solve equation $y'=1-3x+y+x^2+xy$ with another initial value $y(0)=1$. Solve: We solve this by using Newton's extraordinary method.We assume that the solution is analytic,which means it can be expanded in Taylor series.$y(0)=1$ means that $$ y'(0)=2…

学习微分方程中,一个很常见的疑惑就是,我们所熟悉的非齐次微分方程的通解是对应齐次方程的通解加特解,但是更为重要的是,我们需要知道这句话是怎么得来的. 我们探讨一个未知问题的一般思路是将其不断的与已知已解决的问题进行靠拢,关于微分方程,最简单的不过是可分离变量的微分方程,那么我们就尝试将(1)方程与之靠拢. 这样我们就很容易理解文章已开始提出的疑问:一阶非齐次线性方程的通解是对应齐次方程的通解和非齐次方程的特解这句话了.同时也能够很彻底理解一阶非齐次线性方程的通解公式的形式了. 而上面这化腐朽为神…

-------------------------------------------------------------- Chapter 1: Introduction to Discrete Differential Geometry: The Geometry of Plane Curves . A better approximation than the tangent is the circle of curvature. . If the curve is sufficientl…

The author has a course on web: http://brickisland.net/DDGSpring2016/ It has more reading assignments and sliders which are good for you to understand ddg. ------------------------------------------------------------- DISCRETE DIFFERENTIAL GEOMETRY :…

<Differential Geometry of Curves and Surfaces> by Manfredo P. do Carmo real line Rinterval I==============================================CH1 CurvesDEFINITION. A parametrized differentiable curve is a differentiable map a: I --> R3 of [an open in…

<Differential Geometry of Curves and Surfaces> by Manfredo P. do Carmo real line Rinterval I==============================================CH1 CurvesDEFINITION. A parametrized differentiable curve is a differentiable map a: I --> R3 of [an open in…

马丁·福勒-page对象 译者注:这篇文章翻译自马丁·福勒(Martin Flower,对,没错,就是软件教父)官网的一篇文章,原文出处在文底.如果你正在做WEB自动化测试,那么我强烈推荐你看这篇文章.另外透露Martin Flower将于10月份左右来成都ThoughtWorks办公室,大家有机会一睹他的风采. 当你在为web页面编写测试时,你需要操作该web页面上的元素来点击链接或确定显示的内容.然后,如果你在测试代码中直接操作html元素,那么你的代码是机器脆弱的,因为UI会经常变动.一个…

来源: https://zcopy.wordpress.com/ 说明: 本文不是对原文的逐字逐句翻译,而是摘取核心部分以介绍RDMA Send操作(后面凡是提到RDMA send, 都对应于IBA里的send操作).文中给出的例子非常浅显易懂,很值得一读. 1. What is RDMA | 什么是RDMA RDMA is Remote Direct Memory Access which is a way of moving buffers between two applications…

Index Ada Agda Alef Android APL Arduino ASP.NET MVC Assembly Language Non-X86 AutoHotkey Autotools Awk Bash Basic BETA C C# C++ Chapel Cilk Clojure COBOL CoffeeScript ColdFusion Cool Coq D Dart DB2 Delphi / Pascal DTrace Elasticsearch Emacs Erlang F#…

Computational Geometry The Geometry Center (UIUC) Computational Geometry Pages (UIUC) Geometry in Action (UIC) Geometric Resource (UFL) CAGD Applets (UKA) Voronoi/Delaunay Applet (CornellUniversity) Directory of Computational Geometry Software (Dr. N…

最近严重感觉到数学知识的不足! http://bbs.gameres.com/showthread.asp?threadid=10509 [译]Mathematics for Computer Graphics Mathematics for Computer Graphics数学在计算机图形学中的应用Greg Turk, August 1997 “学习计算机图形学需要多少的数学?”这是初学者最经常问的问题.答案取决于你想在计算机图形学领域钻研多深.如果仅仅使用周围唾手可得的图形软件,你不需要知…

Numerous experimental measurements in spatially complex systems have revealed anomalous diffusion in which The mean square displacement scales as a fractional order power law in time. Over the past two decades a new mathematical description has been …

spark集群中的节点可以只处理自身独立数据库里的数据,然后汇总吗? 修改 我将spark搭建在两台机器上,其中一台既是master又是slave,另一台是slave,两台机器上均装有独立的mongodb数据库.我是否可以让它们只统计自身数据库的内容,然后将结果汇总到一台服务器上的数据库里?目前我的代码如下,但是最终只统计了master里的数据,另一个worker没有统计上. val config = new Configuration() //以下代码表示只统计本机数据库上的数据,猜测问题可能…

Mathematics for Computer Graphics 最近严重感觉到数学知识的不足! http://bbs.gameres.com/showthread.asp?threadid=10509 [译]Mathematics for Computer Graphics Mathematics for Computer Graphics数学在计算机图形学中的应用Greg Turk, August 1997“学习计算机图形学需要多少的数学?”这是初学者最经常问的问题.答案取决于你想在计算机…

https://www.quora.com/How-do-I-learn-machine-learning-1?redirected_qid=6578644   How Can I Learn X? Learning Machine Learning Learning About Computer Science Educational Resources Advice Artificial Intelligence How-to Question Learning New Things Lea…

Awesome Courses  Introduction There is a lot of hidden treasure lying within university pages scattered across the internet. This list is an attempt to bring to light those awesome courses which make their high-quality material i.e. assignments, lect…

https://www.quora.com/How-do-I-learn-mathematics-for-machine-learning   How do I learn mathematics for machine learning? Promoted by Time Doctor Software for productivity tracking. Time tracking and productivity improvement software with screenshots…

Recommended Books Here is a list of books which I have read and feel it is worth recommending to friends who are interested in computer science. Machine Learning Pattern Recognition and Machine Learning Christopher M. Bishop A new treatment of classi…

| Main | Site Index | Download | mimetic A free/GPL C++ MIME Library mimetic is a free/GPL Email library (MIME) written in C++ designed to be easy to use and integrate but yet fast and efficient. It is based on the C++ standard library and heavily us…

Github上的1000多本免费电子书重磅来袭!   以前 StackOverFlow 也给出了一个免费电子书列表,现在在Github上可以看到时刻保持更新的列表了. 瞥一眼下面的书籍分类目录,你就能知道这个免费电子书库的含金量了吧.记得一定要看几本,千万别下载了大量书籍而束之高阁! 行动重于空想! Github地址:     https://github.com/vhf/free-programming-books/blob/master/free-programming-books.md I…