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Chapter One Introduction

1.1 Background and Significance

ODE development, the formation of many disciplines are closely linked, for example, geometry branch of mathematics, physics, chemistry, biology, economics and even electronic technology, aerospace, etc. - from the development of ordinary differential equations profound and important influence, particularly the development of computer applications and theoretical study of ordinary differential equations to provide a more powerful tool. To solve practical mathematical problems of many, it is necessary by the inherent characteristics of the relationship between law and observational studies of the actual object seize the principal contradiction and establish a mathematical model reflecting the real problems while on the mathematical model of solving problems, ordinary differential equations is the most important knowledge tools. So to continue to explore application ordinary Differential Equations in mathematical modeling and still it has important academic value and its profound practical significance.

Currently, there are many aspects of the research scholars, for example, Zhu Mei ling in "too far Urban V ocational College News" briefly describes the process of development and mathematical modeling of ordinary differential equations and ordinary differential equations in Mathematical Modeling Some applications, and the status and role of mathematical modeling in mathematics teaching made some prospects; Wang Ying xia in "intelligence" describes the development period December 2011 ordinary differential equations, mathematical modeling characteristics; focuses on ordinary differential equations combined with each other and mathematical modeling, specific examples relevant in different areas, summarized the importance of ordinary Differential Equations in mathematical modeling; Zhao Jia lin in "China Education innovation Herald" 2009 the 1 period describes the objective is an important relationship between the number of mathematical models.

Central subject areas of mathematics ODE has been nearly 300 years of development history, in order to seek to resolve a similar fate during the freefall drop as a function of distance and time; this kind of practical research rocket in the air when the flight path, etc. question often asked us to find that one or more unknowns equations certain conditions, in order to solve such practical problems resulting in a differential

equation. the equation contains the unknown function and unknown function called derivative or differential equations . differential equations is generated in the process of dealing with practical problems, the study of differential equations and facilitate the resolution of practical problems, but also to promote the development of other disciplines.

1.2 The main content of this paper

Based on the mathematical model and the introduction of ordinary differential equations in mathematical modeling applied ordinary differential equations, such as: the general theory of differential equations, existence and uniqueness, stability of differential equations, ordinary differential equation model population, diet mathematical models, chemical plant ventilation issue model. find theoretical study applied mathematics to solve practical problems in the process, while setting up and solving all mathematical models, are designed to better guide the application of mathematical theory in real life. ordinary Differential Equations ordinary Differential Equations and the emergence of wide application in mathematical modeling, is to better enable ordinary people to understand and use mathematical theory, to better solve practical problems. the conversion to a knowledge-based theory of sublimation capacity by type, highlight Differential Equations and applications in mathematical modeling and strive to make a significant contribution to the outstanding in various fields.

Application of Chapter II Ordinary Differential Equations in Mathematical Modeling ODE originate from production practice, develop and gradually improve, with differential equations to solve practical problems is generally divided into the following steps in solving many problems in science and technology: First, the analysis and propose practical problems; second, according to the problem law establishing differential equations (known as the mathematical model); third, the solution of this differential equation or qualitative analysis; the fourth, then the final solution of the equation (or nature) explain and predict the development of mathematical modeling Yes. . the main way to solve practical problems of differential equations modeling approach described below:

Modeling is an important method of differential equations and applied mathematical modeling, mathematical description of many practical problems would lead to solving the problem of definite solution of differential equations. The solution of the problem given all sorts of practical problems of differential equations, in

general, you can press the following steps :

(1) establish the corresponding mathematical model based on the actual problem - - differential equations (group).

(2) research and solving the mathematical model, including the characteristics of the solution.

(3) the use of solution results obtained, in the form of numerical solution, qualitative research and analysis, interpretation of practical problems, in order to predict and describe certain phenomena, and even social phenomena specific characteristics. (4) modify the model if necessary, or to explore the matter further.

Common methods listed equations are:

(1) according to the law column equation, in mathematics, mechanics, physics, chemistry and other disciplines in many natural phenomena have been satisfied by the law for people to grasp, and directly described by differential equations. We often use these laws on certain practical issues Equations are listed.

(2) micro-element analysis method and the integral method takes an arbitrary region There are many phenomena in nature rule is satisfied by the relationship between the infinitesimal variables expressed. For such problems, the use of micro-element analysis, a number of variables (independent variables with unknown function) by the known rules the relationship between the differential element, and then get the differential equation by finding the limits of the method, or equivalently, by integrating the regional approach to establish any differential equations.

(3) simulation approximation

In biology, economics and other disciplines, many phenomena that meet the law is not clear, and quite complicated, and therefore need to know the actual data or a large number of experimental data, put forward various hypotheses. Under certain assumptions, given the actual phenomenon meet the objective law, then list the appropriate differential equations based on mathematical methods in modeling the actual process of differential equations, are often integrated application of the method. In either application modeling methods, usually based on the actual issues in the case, make certain assumptions and simplified, and the theory or model results were compared with the actual situation verified and compared in order to modify the model to make it more accurate description to solve practical problems and thus achieve the purpose of forecasting.

Mathematical Model 2.1 weight loss

1. The question raised

With the improvement of people's living standards, ordinary people in diet fitness wind malpractice, but many of the weight loss methods, food, beverages almost let people know what to do, some not achieve the desired effect, or even adverse consequences, so that newspapers, television, radio constantly remind people: to lose weight should be careful to ask how to build a mathematical model of weight loss.? 2. Analysis

All races of people of different gender has its own weight standards, but for Asians, 20% more than the standard weight considered obese. "Obesity," a sense that too much fat that exceed the standard. If human ingestion of food containing excessive heat, the body of these excess calories will be converted to fat in fat increase. in order to lose weight should eat or not eat it seems, but in order to sustain life, it must consume some energy (heat ) maintain basic metabolism, work, learning and physical exercise also burns calories. Therefore, the weight should be based on proper analysis of diet, metabolism, physical exercise and work on the basis of these relationships, select the appropriate method of mathematical model of weight loss thus we must start to build.

3. The model assumes

(1) Let someone daily caloric intake from food is aJ, where bJ for metabolism (ie automatic consumption), and working life must be consumed per day per kg of body weight J calories, physical activity per kg body weight per day J consumed calories;

(2) a person stored as fat calories of white percent effective, while 1kg of fat calories is 42000J;

(3) Let the weight of time t continuously differentiable function

Chapter summary

Through theoretical and basic study on the stability of differential equations, the study of the basic theory and practical weight loss problem mathematical models, to illustrate the application of mathematics has penetrated into all fields or industries increasingly rely on mathematics. With the social and the development of technology, both in the various disciplines, and in the industry have emerged a large number of urgent need of people to study and resolve the actual problem, which requires the relevant staff the flexibility to use thinking and mathematical knowledge to solve problems encountered, so that the greatest social and economic benefits achieved.

第一章绪论

1.1背景及意义

常微分方程的发展、形成与许多学科都有着密切的联系,例如几何学、物理学、化学、生物学、经济学甚至电子科技、航天航空等.为数学的分支学科—常微分方程的发展起着深刻而重要的影响,特别是计算机的发展更为常微分方程的应用及理论研究提供有力的工具.数学若想解决实际的许多问题,就要通过观察研究实际对象的特征和内在的关系规律,抓住问题的主要矛盾,建立起反映实际问题的数学模型.而在数学模型求解的问题上,常微分方程是最重要的知识工具.因此继续探讨研究常微分方程在数学建模中的应用依然是有着及其重要的学术价值和及其深刻的现实意义.

目前,已有很多学者对此方面进行了研究,例如,朱美玲在《太远城市职业技术学院报》中简要介绍了常微分方程的发展和数学建模的过程以及常微分方程在数学建模中的一些应用,并对数学建模在数学教学中的地位和作用作了一些展望;王英霞在《才智》2011年12期中介绍常微分方程的发展、数学建模的特点;重点介绍了常微分方程与数学建模相互结合,在不同的领域中的相关的具体例子,总结常微分方程在数学建模中的重要性;赵家林在《中国科教创新导刊》2009年第1期中描述了客观是的数量关系的一种重要数学模型.

数学领域的中心学科常微分方程至今已有近300 年的发展历史,为了寻求、解决类似自由落体下落过程中下落距离和时间的函数关系;研究火箭在空中飞行时的飞行轨道等这类实际性的问题,往往就要求我们找到满足某些特定条件的一个或多个未知数方程,为了解决这类实际问题从而产生了微分方程.把含有未知函数及未知函数导数或微分的方程称之为微分方程.微分方程是在处理实际问题的过程中产生的,微分方程的研究又促进实际问题的解决,同时也促进其他学科的发展.

1.2本文研究的主要内容

本文通过对常微分方程、数学模型、以及常微分方程在数学建模中应用的介绍,如:微分方程的一般理论、微分方程解的存在惟一性、微分方程的稳定性问题、人口模型、减肥的数学模型、化工车间的通风问题模型等.发现应用数学理论研究解决实际过程中的问题.而一切数学模型的建立和求解,都是为了更好的应用数学理论指导实际生活.常微分方程的出现以及常微分方程在数学建模中的广泛应用,就是为了更好地使普通人理解并利用数学理论,更好的解决实际中的问题.把理论升华为由知识型向能力型转化,突显微分方程以及微分方程在数学建模中的应用,努力在各个领域做出突出重大贡献.

第二章常微分方程在数学建模中的应用

常微分方程来源于生产实践,在解决科学技术的许多问题中发展并逐步完善,用微分方程解决实际问题一般分为以下几步:第一,实际问题的分析及提出;第二,根据问题的规律建立微分方程(称为建立数学模型);第三,解此微分方程或对方程进行定性分析;第四,最后再用方程的解(或性质)解释并预测问题的发展.数学建模是微分方程解决实际问题的最主要的途径.下面说明建模方法: 微分方程建模是数学建模的重要方法与应用,许多实际问题的数学描述将导致求解微分方程的定解问题.把形形色色的实际问题化微分方程的定解问题,大体上可以按以下几步:

(1)根据实际问题建立对应的数学模型———微分方程(组).

(2) 求解与研究这一数学模型,包括分析解的特征.

(3)利用解得结果,解的形式和数值,进行定性研究与分析,解释实际问题,从而预测和描述某些现象,甚至社会现象中的特定特质.

(4)必要时修改模型或对问题作进一步探讨.

列方程常见的方法有:

(1)按规律列方程,在数学、力学、物理、化学等学科中许多自然现象所满足的规律已为人们所掌握,并直接由微分方程进行描述.我们常利用这些规律对某些实际问题列出微分方程.

(2)微元分析法和任意区域上取积分的方法

自然界中有许多现象所满足的规律是通过变量的微元之间的关系式来表达的.对于这类问题,利用微元分析法,通过已知的规律建立一些变量( 自变量与未知函数) 的微元之间的关系式,然后再通过求极限的方法得到微分方程,或等价地通过任意区域上求积分的方法来建立微分方程.

(3)模拟近似法

在生物、经济等学科中,许多现象所满足的规律并不清楚,而且相当复杂,因而需要了解实际资料或大量的实验数据,提出各种假设.在一定的假设前提下,给出实际现象所满足的客观规律,然后根据适当的数学方法列出微分方程.实际的微分方程建模过程中,也往往是上述方法的综合应用.

不论应用哪种建模方法,通常要根据实际问题中的情况,作出一定的假设与简化,并把模型的理论或计算结果与实际情况进行对照验证和比较,以修改模型使之更准确地描述解决实际问题并进而达到预测预报的目的.

2.1 减肥的数学模型

2.1.1问题的提出

随着人们生活水平的提高,普通百姓中减肥健美之风日盛.但是众多的的减肥手段、食品、饮料几乎让人们不知所措,有的达不到预期的效果,甚至产生不

良的后果,以致报刊、电视、广播经常提醒人们:减肥要慎重.问如何建立减肥的数学模型?

2.1.2问题分析

各种种族的不同性别人都有它自己体重的标准,但对亚洲人来说,超过标准体重的20%视为肥胖.“肥胖”从某种意义上说就是脂肪过多以致超过标准.如果人吸收含过多热量的食物,则人体中这些过多的热量就会转化为脂肪而使脂肪增加.为了减肥应似乎少吃或不吃,但为了维持生命,就必须消耗一定的能量(热量)维持最基本的新陈代谢,工作、学习及体育锻炼也要消耗热量.因此,减肥应基于对饮食、新陈代谢、工作及体育锻炼这些关系的正确分析基础上,选择适当的方法进行.减肥的数学模型就要由此入手来建立.

2.1.3模型假设

(1)设某人每天从食物中摄取的热量是aJ,其中bJ用于新陈代谢(即自动消耗),而从事工作、生活每天每kg体重必须消耗J 的热量,进行体育锻炼每天每kg体重消耗J 的热量;

(2)某人以脂肪形式储存的热量的百分之白的有效,而1kg脂肪含热量是42000J;

(3)设体重是时间t的连续的可微函数

第三章总结

本文通过对微分方程的基本理论及稳定性研究、减肥的数学模型等基本理论及实际问题的研究、说明数学的应用已渗透到各个领域,或者说各行各业日益依赖于数学.随着社会和科技的发展,无论是在各学科,还是在各行业均涌现出了大量的、亟待人们去研究和解决的实际课题.这就要求相关的工作人员能灵活地运用数学的思维方法和知识来解决所遇到的问题,从而取得的最大的社会和经济效益.

中英文参考文献格式

中文参考文献格式 参考文献(即引文出处)的类型以单字母方式标识: M——专著,C——论文集,N——报纸文章,J——期刊文章,D——学位论文,R——报告,S——标准,P——专利;对于不属于上述的文献类型,采用字母“Z”标识。 参考文献一律置于文末。其格式为: (一)专著 示例 [1] 张志建.严复思想研究[M]. 桂林:广西师范大学出版社,1989. [2] 马克思恩格斯全集:第1卷[M]. 北京:人民出版社,1956. [3] [英]蔼理士.性心理学[M]. 潘光旦译注.北京:商务印书馆,1997. (二)论文集 示例 [1] 伍蠡甫.西方文论选[C]. 上海:上海译文出版社,1979. [2] 别林斯基.论俄国中篇小说和果戈里君的中篇小说[A]. 伍蠡甫.西方文论选:下册[C]. 上海:上海译文出版社,1979. 凡引专著的页码,加圆括号置于文中序号之后。 (三)报纸文章 示例 [1] 李大伦.经济全球化的重要性[N]. 光明日报,1998-12-27,(3) (四)期刊文章 示例 [1] 郭英德.元明文学史观散论[J]. 北京师范大学学报(社会科学版),1995(3). (五)学位论文 示例 [1] 刘伟.汉字不同视觉识别方式的理论和实证研究[D]. 北京:北京师范大学心理系,1998. (六)报告 示例 [1] 白秀水,刘敢,任保平. 西安金融、人才、技术三大要素市场培育与发展研究[R]. 西安:陕西师范大学西北经济发展研究中心,1998. (七)、对论文正文中某一特定内容的进一步解释或补充说明性的注释,置于本页地脚,前面用圈码标识。 参考文献的类型 根据GB3469-83《文献类型与文献载体代码》规定,以单字母标识: M——专著(含古籍中的史、志论著) C——论文集 N——报纸文章 J——期刊文章 D——学位论文 R——研究报告 S——标准 P——专利 A——专著、论文集中的析出文献 Z——其他未说明的文献类型 电子文献类型以双字母作为标识: DB——数据库 CP——计算机程序 EB——电子公告

化工英文文献翻译

Heavy Oil Development Technology of Liaohe Oilfield Han Yun (Scientific Research Information Department Exploration&Development Research Institute,Liaohe Oilfield Company) Liaohe Oilfield,the largest heavy oil production base in China,features in various reservoir types,deep burial,and wide range of crude oil viscosity.For many years,a series of technologies have been developed for different oil products and reservoir types of the oilfield,of which water flooding,foam slug drive,steam stimulation,steam drive,and SAGD are the main technologies. After continuous improvement,they have been further developed and played an important role in the development of heavy oil in the oilfield. Liaohe Oilfield is abundant in heavy oil resources,46%of the total proved reserves of Liaohe Oilfield Company. Horizontally the resources concentrates in the West Depression and the southern plunging belt of the Central Uplift in Liaohe Rift. Vertically,it is mainly distributed in Paleocene Shahejie Formation(ES). The distinctive geological feature of Liaohe 0ilfield is manifested in three aspects:first,the heavy oil reservoirs are deeply buried and 80%of them are buried more than 900m deep;second,the heavy oil viscosity ranges widely.For most of the reservoirs.the dead oil viscosity ranges in 100~100000mPa·s with the maximum 650000mPa·s.Third the reservoir types are various with complicated oil—water relationship,most of the reservoirs are edge water and bosom water reservoirs and there are also edge water reservoirs,top water reservoirs and bosom water reservoirs.For more than 20 years of development,Liaohe Oilfield has developed series of heavy oil development technologies for different oil products and different types of reservoirs,such as water flooding, foam slug drive,steam stimulation steam drive and SAGD.The most difficult issues have been overcome in the development of the super

100篇英文经典文献

share with 各位会计、财务专业的同学... (P.S.读英文期刊绝对是体力活...开读前一定要吃好睡好...) 这些是会计学的基础文献,是所有其他文献的参考文献~~~ 经典文献(The 100 articles with the highest citation index-until 1996) 参考:Lawrence D. Brown, 1996, “Influential Accounting Articles, Individuals, Ph. D Granting Institutions and Faculties; A Citational Analysis”, Accounting, Organizations and Society, Vol.21, NO.7/8, P726-728 1. Ball, R. and Brown, P., 1968, “An Empirical Evaluation of Accounting Income Numbers”, journal of Accounting Research, Autumn, pp. 159-178 1. 2.Watts R.L., Zimmerman J., 1978, “Towards a Positive Theory of the Determination of Accounting Standards”, The Ac counting Review, pp. 112-134 2. 3.Healy P.M, 1985, “The Effect of Bonus Schemes on Accounting Decisions”, Journal of Accounting and Economics, April, 85-107 3.Hopwood A. G., “Towards an Organizational Perspective for the Study of Accounting and Information S ystems”, Accounting, Organizations and Society (No. 1, 1978) pp. 3-14 4.Collins, D. W., Kothari, S. P., 1989, “An Analysis of Intertemporal and Cross-Sectional Determinants of Earnings Response Coefficients”, journal of Accounting & Economics, pp. 143-181 5.EastonP.D, Zmijewski M.E, 1989, “Cross-Sectional Variation in the Stock Market Response to Accounting Earnings Announcements”, Journal of Accounting and Economics, 117-141 6.Beaver, W. H., 1968, “The Information Content of Annual Earnings Announcements”, jo urnal of Accounting Research, pp. 67-92 7.Holthausen R.W., Leftwich R.W., 1983, “The Economic Consequences of Accounting Choice: Implications of Costly Contracting and Monitoring”, journal of Accounting & Economics, August, pp77-117 8.Patell J.M, 1976, “Corp orate Forecasts of Earnings Per Share and Stock Price Behavior: Empirical Tests. Journal of Accounting Research, Autumn, 246-276 9.Brown L.D., Griffin P.A., Hagerman R.L., Zmijewski M.E, 1987, “An Evaluation of Alternative Proxies for the Market’s Assessment of Unexpected Earnings”, Journal of Accounting and Economics, 61-87 10.Ou J.A., Penman S.H., 1989, “Financial Statement Analysis and the Prediction of Stock Returns”, Journal of Ac counting and Economics, Nov., 295-329 11.William H. Beaver, Roger Clarke, William F. Wright, 1979, “The Association between Unsystematic Security Returns and the Magnitude of Earnings Forecast Errors,” Journal of Accounting Research, 17, 316-340.

英文文献及中文翻译

毕业设计说明书 英文文献及中文翻译 学院:专 2011年6月 电子与计算机科学技术软件工程

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石油和天然气勘探中英文对照外文翻译文献

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中英文对照资料外文翻译文献

中英文对照资料外文翻译文献 平设计任何时期平面设计可以参照一些艺术和专业学科侧重于视觉传达和介绍。采用多种方式相结合,创造和符号,图像和语句创建一个代表性的想法和信息。平面设计师可以使用印刷,视觉艺术和排版技术产生的最终结果。平面设计常常提到的进程,其中沟通是创造和产品设计。共同使用的平面设计包括杂志,广告,产品包装和网页设计。例如,可能包括产品包装的标志或其他艺术作品,举办文字和纯粹的设计元素,如形状和颜色统一件。组成的一个最重要的特点,尤其是平面设计在使用前现有材料或不同的元素。平面设计涵盖了人类历史上诸多领域,在此漫长的历史和在相对最近爆炸视觉传达中的第20和21世纪,人们有时是模糊的区别和重叠的广告艺术,平面设计和美术。毕竟,他们有着许多相同的内容,理论,原则,做法和语言,有时同样的客人或客户。广告艺术的最终目标是出售的商品和服务。在平面设计,“其实质是使以信息,形成以思想,言论和感觉的经验”。

在唐朝(618-906 )之间的第4和第7世纪的木块被切断打印纺织品和后重现佛典。阿藏印在868是已知最早的印刷书籍。在19世纪后期欧洲,尤其是在英国,平面设计开始以独立的运动从美术中分离出来。蒙德里安称为父亲的图形设计。他是一个很好的艺术家,但是他在现代广告中利用现代电网系统在广告、印刷和网络布局网格。于1849年,在大不列颠亨利科尔成为的主要力量之一在设计教育界,该国政府通告设计在杂志设计和制造的重要性。他组织了大型的展览作为庆祝现代工业技术和维多利亚式的设计。从1892年至1896年威廉?莫里斯凯尔姆斯科特出版社出版的书籍的一些最重要的平面设计产品和工艺美术运动,并提出了一个非常赚钱的商机就是出版伟大文本论的图书并以高价出售给富人。莫里斯证明了市场的存在使平面设计在他们自己拥有的权利,并帮助开拓者从生产和美术分离设计。这历史相对论是,然而,重要的,因为它为第一次重大的反应对于十九世纪的陈旧的平面设计。莫里斯的工作,以及与其他私营新闻运动,直接影响新艺术风格和间接负责20世纪初非专业性平面设计的事态发展。谁创造了最初的“平面设计”似乎存在争议。这被归因于英国的设计师和大学教授Richard Guyatt,但另一消息来源于20世纪初美国图书设计师William Addison Dwiggins。伦敦地铁的标志设计是爱德华约翰斯顿于1916年设计的一个经典的现代而且使用了系统字体设计。在20世纪20年代,苏联的建构主义应用于“智能生产”在不同领域的生产。个性化的运动艺术在2俄罗斯大革命是没有价值的,从而走向以创造物体的功利为目的。他们设计的建筑、剧院集、海报、面料、服装、家具、徽标、菜单等。J an Tschichold 在他的1928年书中编纂了新的现代印刷原则,他后来否认他在这本书的法西斯主义哲学主张,但它仍然是非常有影响力。Tschichold ,包豪斯印刷专家如赫伯特拜耳和拉斯洛莫霍伊一纳吉,和El Lissitzky 是平面设计之父都被我们今天所知。他们首创的生产技术和文体设备,主要用于整个二十世纪。随后的几年看到平面设计在现代风格获得广泛的接受和应用。第二次世界大战结束后,美国经济的建立更需要平面设计,主要是广告和包装等。移居国外的德国包豪斯设计学院于1937年到芝加哥带来了“大规模生产”极简到美国;引发野火的“现代”

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