(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…

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…

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…

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…

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…

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…

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…

Exercises for IN1900October 14, 2019PrefaceThis document contains a number of programming exercises made for the courseIN1900. The chapter numbers and titles correspond to the chapters of the book“A primer on Scientific Programming with Python” by Ha…

备注: 1.先要安装wheel库:pip install wheel 2.下载wheel,切换至下载路径,然后安装:pip install wheel库名.whl Windows Python Extension Packages by Christoph Gohlke, Laboratory for Fluorescence Dynamics, University of California, Irvine. HoloPy, a tool for working with digital h…

http://www.boost.org/doc/libs/1_61_0/ Boost 1.61.0 Library Documentation Accumulators Framework for incremental calculation, and collection of statistical accumulators. Author(s): Eric Niebler First Release: 1.36.0 Standard: Categories: Math and nume…

Unofficial Windows Binaries for Python Extension Packages by Christoph Gohlke, Laboratory for Fluorescence Dynamics, University of California, Irvine. This page provides 32- and 64-bit Windows binaries of many scientific open-source extension package…

小白往往听到微分方程就觉得害怕,其实数学建模中的微分方程模型不仅没那么复杂,而且很容易写出高水平的数模论文. 本文介绍微分方程模型边值问题的建模与求解,不涉及算法推导和编程,只探讨如何使用 Python 的工具包,零基础求解微分方程模型边值问题. 通过 3个 BVP 案例层层深入,手把手教你搞定微分方程边值问题. 欢迎关注『Python小白的数学建模课 @ Youcans』系列,每周持续更新 1. 常微分方程的边值问题(BVP) 1.1 基本概念 微分方程是指含有未知函数及其导数的关系式. 微分…

-------------------------------------------------------------- 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…

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…

sklearn实战-乳腺癌细胞数据挖掘(博主亲自录制视频教程) https://study.163.com/course/introduction.htm?courseId=1005269003&utm_campaign=commission&utm_source=cp-400000000398149&utm_medium=share 医药统计项目可联系 QQ:231469242 http://www.kancloud.cn/wizardforcel/scipy-lecture-n…

| 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…

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#…

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…

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…

Kaiming He, Xiangyu Zhang, Shaoqing Ren, Jian Sun           Microsoft Research {kahe, v-xiangz, v-shren, jiansun}@microsoft.com Abstract摘要 Deeper neural networks are more difficult to train. We present a residual learning framework to ease the traini…

和 Nested Partition 有相通之处? 伯克利提出 AdaSearch:一种用于自适应搜索的逐步消除方法 在机器学习领域的诸多任务当中,我们通常希望能够立足预先给定的固定数据集找出问题的答案.然而,在某些应用场景下我们并没有先验数据可供参考 ; 相反,我们必须自行收集数据以回答那些自己感兴趣的问题.举例来说,这种情况在环境污染物监测以及人口普查类调查中就比较常见.自行收集数据的方式,使得我们能够将注意力集中在相关度最高的信息来源身上.然而,确定哪些信息来源能够生成有用的指标同样不是件…

8.02  Physics II (电磁学基础) Introduction to electromagnetism and electrostatics: electric charge, Coulomb's law, electric structure of matter; conductors and dielectrics. Concepts of electrostatic field and potential, electrostatic energy. Electric curr…

GNU scientific library 是一个强大的C,C++数学库.它涉及的面很广,并且代码效率高,接口丰富.正好最近做的一个项目中用到多元高斯分布,就找到了这个库. GNU scientific library下载地址:http://ftpmirror.gnu.org/gsl/ 相应说明文档下载地址: http://www.gnu.org/software/gsl/manual/gsl-ref.ps.gz 编译时需要加上一些后缀: g++ xxx.cpp -lgsl -lgslcbla…

function [sys,x0,str,ts,simStateCompliance] = sfuntmpl(t,x,u,flag) %SFUNTMPL General MATLAB S-Function Template % With MATLAB S-functions, you can define you own ordinary differential % equations (ODEs), discrete system equations, and/or just about %…

注意:因为页面显示原因.里头的公式没能做到完美显示,有须要的朋友请到我的资源中下载 无需进行又一次初始化的水平集演化:一个新的变分公式 Chunming Li , Chenyang Xu , Changfeng Gui , and Martin D. Fox 1.Department of Electrical and 2.Department of Imaging 3.Department of Mathematics Computer Engineering      and Visuali…