In general differential calculus, we have learned the definitions of function continuity, such as functions of class \(C^0\) and \(C^2\). For most cases, we only take them for granted as for example, we have memorized the formulations of Green identi…

Understanding of continuity definition in topology When we learn calculus in university as freshmen, we are usually force-fed with the \(\epsilon-\delta\) language for the definition of a function’s continuity, i.e. A function \(f: A \rightarrow \mat…

This post summarises different ways of constructing continuous functions, which are introduced in Section 18 of James Munkres "Topology". Constant function. Inclusion function. N.B. The function domain should have the subspace topology relative…

One of the most striking facts about neural networks is that they can compute any function at all. That is, suppose someone hands you some complicated, wiggly function, f(x)f(x): No matter what the function, there is guaranteed to be a neural network…

      Deep Deterministic Policy Gradients in TensorFlow AUG 21, 2016 This blog from: http://pemami4911.github.io/blog/2016/08/21/ddpg-rl.html Introduction Deep Reinforcement Learning has recently gained a lot of traction in the machine learning commu…

<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…

In recent years, Kernel methods have received major attention, particularly due to the increased popularity of the Support Vector Machines. Kernel functions can be used in many applications as they provide a simple bridge from linearity to non-linear…

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 Ratio Test Consider the series $\sum_{n=0}^\infty a_n$ where each term $a_n$ i…

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,…

Milan Ikits University of Utah Joe Kniss University of Utah Aaron Lefohn University of California, Davis Charles Hansen University of Utah This chapter presents texture-based volume rendering techniques that are used for visualizing three-dimensional…