latex实验报告模板

differential and integral equations的latex模板1. 引言1.1 概述微分方程和积分方程是数学中重要的研究课题之一。

它们的应用广泛涉及物理学、工程学、经济学等领域。

微分方程描述了包含导数的函数关系，而积分方程则涉及到未知函数与其积分之间的关系。

在许多实际问题中，我们常常需要找到这种关于未知函数及其导数或积分之间的关系，以进一步解决问题。

因此，深入了解微分方程和积分方程的定义、性质以及求解方法对于解决实际问题具有重要意义。

1.2 文章结构本文将围绕微分方程和积分方程展开探讨。

首先，在第2节中介绍微分方程，包括定义和基本概念。

我们将探讨不同类型的微分方程，并详细说明它们的特点和应用领域。

接着，在第3节中介绍积分方程，同样包括定义和基本概念。

我们将介绍几种常见类型的积分方程，并讨论求解这些方程的方法。

在第4节中，我们将探讨微分和积分方程在物理学、工程学和经济学领域的应用。

这些应用涵盖了广泛的实际问题，包括物体运动、电路分析、经济增长等。

我们将深入研究这些应用案例，并说明微分和积分方程在解决这些问题中的作用和意义。

最后，在第5节中进行结论与展望。

我们将对全文进行总结，强调微分方程和积分方程的重要性，并展望未来在该领域的研究方向。

1.3 目的本文的目的是介绍微分方程和积分方程的基本概念、求解方法以及在不同领域中的应用。

通过对这两类方程进行深入研究，读者可以更好地理解它们在数学和实际问题中的重要性，并掌握相应的求解技巧。

同时，我们希望为未来相关研究提供一定的参考和启示，促进该领域的进一步发展。

2. Differential equations（微分方程）2.1 定义和基本概念微分方程是描述自变量与其相应导数之间关系的方程。

它可用于描述物理、工程以及其他科学领域中的各种现象和过程。

一般地，微分方程可以分为常微分方程（ODE）和偏微分方程（PDE）。

常微分方程涉及单个自变量，在解决包含一个未知函数及其导数的问题时非常有用；而偏微分方程涉及多个自变量，在解决包含多个未知函数及其偏导数的问题上是必需的。

latex,英文书,模板篇一：英文SCI论文写作利器latex——宏包latex用法设置行间距的方法：%\setlength{\baselineskip}{15pt}\renewcommand{\baselinestretch}{1}2.去掉容差报警的方法：\hbadness=10000 \tolerance=10000 \hfuzz=150pt3.更改子级item，enumerate的图标的方法：\renewcommand{\labelenumii}{(\arabic{enumii}).}\renewcommand{\labelenumiii}{[\arabic{enumiii}]} \renewcommand{\labelenumiv}{}\renewcommand{\labelitemi}{\PlusCenterOpen } \renewcommand{\labelitemii}{\Checkmark }\renewcommand{\labelitemiii}{\ding {43} }\renewcommand{\labelitemiv}{$\clubsuit$}4.使用下划线，删除线的方法：\usepackage{ulem}\uwave \sout \uwave{.....} \sout{...}如果用中文，应该是包，不然不会正确分行。

如：\usepackage{CJKulem} LaTex会自动给CJKulem加上.sty的后缀\d a 给文字a下面加点，如下： \d G \d P \d I \d I \d O\xout:斜删除线\sout :水平删除线\uwave:波浪线\uline,\uuline:下划线，双下划线\renewcommand{\baselinestretch}{}\renewcommand{\ULdepth} 可以手工修改下划线离基线的距离。

5.高亮，加行号源代码的方法：\usepackage{color}\definecolor{gray}{rgb}{,,}\usepackage{listings}\lstset{numbers=left} \lstset{language=C++} \lstset{breaklines}\lstset{extendedchars=false} \lstset{backgroundcolor=\color{gray}}\lstset{keywordstyle=\color{blue}\bfseries} \lstset{frame=none}\lstset{tabsize=4} \lstset{commentstyle=\color{red}}\lstset{stringstyle=\emph}6.制表位画简单表：\begin{tabbing}..........\=............\=..........\\....\> .........\>.........\\.....\>..........\>.........\\...........\>........\>....\end{tabbing}7.盒子：\mbox{看什么看，死鸟} \fbox{看什么看，死鸟}\fbox 有一个外框\framebox[宽度][位置]{.....}位置：l:左对齐 r:右对齐 s:伸展文本\framebox[][l]{.........}\framebox[3cm][s]{XXX \dotfill XXX}8.点填充：\dotfill\framebox[3cm][s]{XXX \dotfill XXX}9.对单个字母加上斜划线的方法：\makebox[0pt][l]{/}S10.给文本加上边注：............... \marginpar{这是边注一个}......................\marginpar{...\\....\\....}..... ....加上竖线作边注：\marginpar{\rule[Y轴方向坐标：+向上,-向下]{竖线宽度}{竖线长度}}\marginpar{\rule[-]{10mm}{20mm}}:\begin{verbatim}...........\end{verbatim}\begin{verbatim}* ...........\end{verbatim*}将空格也显示也来。

latex英文模板\documentclass{article}\usepackage{graphicx}\usepackage[round]{natbib}\bibliographystyle{plainnat}\usepackage[pdfstartview=FitH,%bookmarksnumbered=true,bookmarksopen=true,%colorlinks=true,pdfborder=001,citecolor=blue,%linkcolor=blue,urlcolor=blue]{hyperref}\begin{document}\title{Research plan under the Post-doctorate program at xx University}%\subtitle{aa}\author{Robert He}\date{2008/04/23}\maketitle\section{Research Title}~~~~Crustal seismic anisotropy in the xx using Moho P-to-S converted phases.\section{Research Background \& Purposes}~~~~Shear-wave splitting analyses provide us a new way to study the seismic structure and mantle dynamics in the crust and mantle. The crustal anisotropy is developed due to various reasons including lattice-preferred orientation (LPO) of mineral crystals and oriented cracks.\newlineTraditionally, the earthquakes occurring in the curst and the subducting plates are selected to determine the seismic anisotropy of the crust. However, none of these methods can helpus to assess the anisotropy in the whole crust. Because crustal earthquakes mostly are located in the upper crust, they do not provide information of lower crust. On the other hand, earthquakes in the subducting plates provide information of the whole crust but combined with upper mantle. However, it’s difficult to extract the sole contri bution of the crust from the measurement. Fortunately P-to-S converted waves (Ps) at the Moho are ideal for investigation of crustal seismic anisotropy since they are influenced only by the medium above the Moho.Moho. Figure \ref{crustalspliting}~schematically shows the effects of shear wave splitting on Moho Ps phases. Initially, a near-vertically incident P wave generates a radially polarized converted shear wave at the crust-mantle boundary. The phases, polarized into fast and slow directions, progressively split in time as they propagate through the anisotropic media. Here, the Ps waves can be obtained from teleseismic receiver function analysis.%%\begin{figure}[htbp]\begin{center}\includegraphics[width=0.47\textwidth]{crustalsplit.png}\caption{The effects of shear wave splitting in the Moho P to S converted phase. Top shows a schematic seismogram in the fast/slow coordinate system with split horizontal Ps components.(cited from: McNamara and Owens, 1993)} \label{crustalspliting}\end{center}\end{figure}%%The Korean Peninsula is composed of three major Precambrian massifs, the Nangrim, Gyeongii, and Yeongnam massifs(Fig.\ref{geomap}). The Pyeongbuk-Gaema Massif forms the southern part of Liao-Gaema Massif of southern Manchuria, and the Gyeonggi and Mt. Sobaeksan massifs of the peninsula are correlated with the Shandong and Fujian Massifs of China.%\begin{figure}[htbp]\begin{center}\includegraphics[width=0.755\textwidth]{geo.png}\caption{Simplified geologic map. NCB: North China block; SCB: South China block.(cited from: Choi et al., 2006)} \label{geomap}\end{center}\end{figure}%Our purpose of the study is to measure the shear wave splitting parameters in the crust of the Korean Peninsula. The shear wave splitting parameters include the splitting time of shear energybetween the fast and slow directions, as well as fast-axis azimuthal direction in the Korean Peninsula. These two parameters provide us constraints on the mechanism causing the crustal anisotropy. From the splitting time, the layer thickness of anisotropy will be estimated. Whether crustal anisotropy mainly contributed by upper or lower crustal or both will be determined. Based on the fast-axis azimuthal direction, the tectonic relation between northeastern China and the Korean peninsula will be discussed.\section{Research Methods}~~~~Several methods have been introduced for calculation of receiver functions. An iterative deconvolution technique may be useful for this study since it produces more stable receiver function results than others. The foundation of the iterative deconvolution approach is aleast-squares minimization of the difference between the observed horizontal seismogram and a predicted signal generated by the convolution of an iteratively updated spike train with the vertical-component seismogram. First, the vertical component is cross-correlated with the radial component to estimate the lag of the first and largest spike in the receiver function (the optimal time is that of the largest peak in the absolute sense in the cross-correlation signal). Then the convolution of the current estimate of the receiver function with the vertical-component seismogram is subtracted from the radial-component seismogram, and the procedure is repeated to estimate other spike lags and amplitudes. With each additional spike in the receiver function, the misfit between the vertical and receiver-function convolution and the radial component seismogram is reduced, and the iteration halts when the reduction in misfit with additional spikes becomes insignificant.\newlineFor all measurement methods of shear-wave splitting, time window of waveform should be selected. Conventionally the shear-wave analysis window is picked manually. However, manual window selection is laborious and also very subjective; in many cases different windows give very different results.\newlineIn our study, the automated S-wave splitting technique willbe used, which improves the quality of shear-wave splitting measurement and removes the subjectivity in window selection. First, the splitting analysis is performed for a range of window lengths. Then a cluster analysis isapplied in order to find the window range in which the measurements are stable. Once clusters of stable results are found, the measurement with the lowest error in the cluster with the lowest variance is presented for the analysis result.\section{Expected results \& their contributions}~~~~First, the teleseismic receiver functions(RFs) of all stations including radial and transverse RFs can be gained. Based on the analysis of RFs, the crustal thickness can be estimated in the Korean Peninsula. Then most of the expected results are the shear-wave splitting parameters from RFs analysis in the crust beneath the Korean Peninsula. The thickness of anisotropic layer will be estimated in the region when the observed anisotropy is assumed from a layer of lower crustal material.All the results will help us to understand the crustal anisotropy source.\newlineCrustal anisotropy can be interpreted as an indicator of the crustal stress/strain regime. In addition, since SKS splitting can offer the anisotropy information contributed by the upper mantle but combined with the crust, the sole anisotropy of the upper mantle can be attracted from the measurement of SKS splitting based on the crustal splitting result.%\cite{frogge2007}%%%\citep{frogge2008}%%%\citep{s-frogge2007}% 5. References\begin{thebibliography}{99}\item Burdick, L. J. and C. A. Langston, 1977, Modeling crustal structure through the use of converted phases in teleseismic body waveforms, \textit{Bull. Seismol. Soc. Am.}, 67:677-691.\item Cho, H-M. et al., 2006, Crustal velocity structure across the southern Korean Peninsula from seismic refraction survey, \textit{Geophy. Res. Lett.} 33, doi:10.1029/2005GL025145.\item Cho, K. H. et al., 2007, Imaging the upper crust of the Korean peninsula by surface-wave tomography, \textit{Bull. Seismol. Soc. Am.}, 97:198-207.\item Choi, S. et al., 2006, Tectonic relation between northeastern China and the Korean peninsula revealed by interpretation of GRACE satellite gravity data, \textit{Gondwana Research}, 9:62-67.\item Chough, S. K. et al., 2000, Tectonic and sedimentary evolution of the Korean peninsula: a review and new view, \textit{Earth-Science Reviews}, 52:175-235.\item Crampin, S., 1981, A review of wave motion in anisotropic and cracked elastic-medium, \textit{Wave Motion}, 3:343-391.\item Fouch, M. J. and S. Rondenay, 2006, Seismic anisotropy beneath stable continental interiors, \textit{Phys. Earth Planet. Int.}, 158:292-320.\item Herquel, G. et al., 1995, Anisotropy and crustal thickness of Northern-Tibet. New constraints for tectonic modeling, \textit{Geophys. Res. Lett.}, 22(14):1 925-1 928.\item Iidaka, T. and F. Niu, 2001, Mantle and crust anisotropy in the eastern China region inferred from waveform splitting of SKS and PpSms, \textit{Earth Planets Space}, 53:159-168.\item Kaneshima, S., 1990, Original of crustal anisotropy: Shear wave splitting studies in Japan, \textit{J. Geophys. Res.}, 95:11 121-11 133.\item Kim, K. et al., 2007, Crustal structure of the Southern Korean Peninsula from seismic wave generated by large explosions in 2002 and 2004, \textit{Pure appl. Geophys.}, 164:97-113.\item Kosarev, G. L. et al., 1984, Anisotropy of the mantle inferred from observations of P to S converted waves, \textit{Geophys. J. Roy. Astron. Soc.}, 76:209-220.\item Levin, V. and J. Park, 1997, Crustal anisotropy in the Ural Mountains foredeep from teleseismic receiver functions, \textit{Geophys. Res. Lett.}, 24(11):1 283 1286.\item Ligorria, J. P. and C. J. Ammon, 1995, Iterative deconvolution and receiver-function estimation. \textit{Bull. Seismol. Soc. Am.}, 89:1 395-1 400.\item Mcnamara, D. E. and T. J. Owens, 1993, Azimuthal shear wave velocity anisotropy in the basin and range province using Moho Ps converted phases, \textit{J. Geophys. Res.}, 98:12 003-12 017.\item Peng, X. and E. D. Humphreys, 1997, Moho dip and crustal anisotropy in northwestern Nevada from teleseismic receiver functions, \textit{Bull. Seismol. Soc. Am.}, 87(3):745-754.\item Sadidkhouy, A. et al., 2006, Crustal seismic anisotropy in the south-central Alborz region using Moho Ps converted phases, \textit{J. Earth \& Space Physics}, 32(3):23-32.\item Silver, P. G. and W. W. Chan, 1991, Shear wave splitting and subcontinental mantle deformation, \textit{J. Geophys. Res.},96:16 429-16454.\item Teanby, N. A. et al., 2004, Automation of shear wavesplitting measurement using cluster analysis, \textit{Bull. Seismol. Soc. Am.}, 94:453-463.\item Vinnik, L. and J-P. Montagner, 1996, Shear wave splitting in the mantle Ps phases,\textit{Geophys. Res. Lett.}, 23(18):2 449- 2 452.\item Yoo, H. J. et al., 2007, Imaging the three-dimensional crust of the Korean peninsula by joint inversion of surface-wave dispersion of teleseismic receiver functions, \textit{Bull. Seismol. Soc. Am.}, 97(3):1 002-1 011.\item Zhu, L., and H. Kanamori, 2000, Moho depth variation in Southern California from teleseismic receiver functions, \textit{J. Geophys. Res.}, doi :10.1029/1999JB900322, 105:2 969-2 980.%%%%\end{document}。

Latex 实用例子通过实验本例子可以基本掌握科技排版的方法：\documentclass[twocolumn]{article}\usepackage{amsmath}\renewcommand{\rmdefault}{ptm}\begin{document}\title{Physical Model Order Reduction}\author{Qiang Wang and Guo-Hua Li\\Department of Electronic Engineering,the East University of China}\date{December 17, 2009}\maketitle\begin{abstract}This paper presents a novelapproach for model order reduction for multilayer lossy RFembedded passives.\end{abstract}\section{Introduction}As the Radiofrequency modules having been designed more compactthan ever before, the parasitic effects due to the tightly coupledinter-connections on the circuit layout are inevitable. Therefore,an efficient method that can derive a circuit model of such circuitlayout is highly desirable. A few techniques such as PEEC were developed to extract equivalent circuits from an electromagnetic model.Classic PEEC solver converts the layout into lumped RLCinterconnection networks, including mutual couplings. Once a circuit model is generated, any circuit solver, such as SPICE, can manage the rest of the job. Unfortunately, the numbers of nodes and elements in the circuits are excessive. Therefore, researchers have been searching for an effective measure that can reduce the model order for accelerating the analysis of the circuit model.Although exploited Krylovsubspace methods and provided ways to speed up the simulation; they all lack the physical insight. In fact, they are mathematics-based MOR. Several realizable model order reduction approaches are also proposed. However, can only handle RC networks. Besides, they both concern with matching the first two or three moments of the system via Taylor's expansion. Thus, these methods can not provide a clear physical explanation to the reduced circuit either. It is worth mentioning that has showed some insight fordealing with coupled inductances, even though the complexity of the scheme itself might have already limited its practical use.The work presented in this paper is an extension to,in which a derived physically realizable lossless expressive circuit model reduction method is introduced. In this paper, a lossy modelis the major concern. The passivity of the resultant circuit modelby the new reduction scheme is guaranteed.\section{Theory}The circuit model generated by traditional quasi-static PEEC model for a multi-layer circuit layout with very thin conducting stripscan easily incorporate the conducting loss, which is a major origin of the circuit loss.Since the meshes used in solving MPIE (Mixed Potential Integrated Equations of the PEEC algorithm are all in regular shapes, thus we could first evaluate their losses piecewisely and then superimpose this pre-calculated loss model to the generated circuit model to represent the conductor loss of the circuit. Therefore reasonable and time-saving approaches to calculate the loss for different meshing geometries are investigated.Since the conductor loss is generally determined by the skin depth effect at RF frequency, a coarse but rapid approximation to this type of loss is to find out the skin depth and other shape factorsof the mesh. Then the equivalent surface impedance can be easily calculated by $R_{L} = l / 2\delta S$, where $l$ is the mesh length, along which the current flows, $S$ is the area of the equivalent crossing section where the current goes through, $\delta$ is the skin depth:\begin{align}\delta=\frac{1}{\sqrt{\smash[b]{\pi f \mu \sigma}}},\label{Equ1}\end{align}in which $f$ is the frequency, $\mu$ is the magnetic permeability, and $\sigma$ is the conductivity of the metal. In addition to this, various other empirical formulas, such as those incould also be used todetermine the conducting loss.Capacitor's loss is mainly due to bypassing leak-age current. Considering the basic relationship be-tween the current and the charge stored in the capacitor, its losscontribution could be computed by $G_{C} = \sigma C / \varepsilon$, where $G_{C}$ is the bypassing conductance, $C$ is the capacitance, $\varepsilon$ and $\sigma$ are the dielectric constant and the conductivity of the substrate, respectively....\end{document}形成的PDF效果图：。