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专业英语论文

专业英语论文
专业英语论文

专业英语培训论文

学院:数学与信息科学学院

专业:信息与计算科学

学号:08102209

姓名:罗书云

指导老师:张美英

2011-6-18

一、专业词汇

1 abel inequality

2 abel summation method

3 abelian equation

4 abelian functor

5 abelian groupoid

6 abridged notation

7 abscissa 8 abscissa of absolute convergence 9 abscissa of summability

10 absolute address 11 absolute coding 12 absolute conic

13 absolute curvature vector 14 absolute differential calculus 15 absolute frequency

16 absolute geometry 17 abstraction operator 18 accelerated motion

19 acceleration of convergence 20 acceleration of gravity 21 access speed

22 accessible boundary point 23 accidental error 24 accumulated error

25 accuracy grade 26 accuracy of measurement 27 acnod

28 adjoint vector 29 adjunct 30 admissibility limit

31 admissible category 32 admissible decision rule 33 admissible homomorphism 34 admissible sequence 35 admissible subgroup 36 affine differential geometry 37 affine function 38 affine length 39 affine rational transformation

40 allowable error 41 alpha capacity 42 angular frequency

43 angular metric 44 decimal part 45 decimal representation

46 decomposable matrix 47 dense in itself set 48 denseness of set

49 dependent equations 58 derivability 51 derivation

52 derivative of higher order 53 difference differential equation 54 derived functor 55difference quotient 56 differentiable function 57differential and integral calculus

58 elliptic motion 59 elliptic orbit 60 elliptic system

61empty mapping 62 empty set 63 endless

64 equivalent equation 65 equivalent functions 66 equivalent proposition

67 error analysis 68 error coefficient 69 exactitude

70 exchange integral 71 exchange theorem 72 extremal function

73 extremal point 74face of a polyhedron 75 factor analysis

76 finite cyclic group 77 finite field 78 focal plane

79 folium of descartes 80 formula 81 formula of propositional logic

82 foundation of geometry 83 first integral 84 formula of propositional logic

85 functional 86 functional analysis 87 functional dependence

88 functional matrix 89 gaussian sum 90 general polynomial

91 general reciprocal 92 general solution 93 greater than or equal to

94 harmonic analyzer 95 homogeneous equation 96 homogeneous function

97 homogeneous integral equation 98 homogeneous lineare transformation

99hyperbolic cosine

100 implicit function 101 improper limit value 102 indivisible

103 induction method 104 interpolation 105 interpolation formula

106 interpolation of operators 107 intersecting lines 108 invertible element 109 invertible map 110 irrational 111 irrational fraction

112 iterate 113 lagrangian function 114 left coset

115 limitless 116 mathematical analysis 117 matricial rank

118 median 119 mu continuity 120 mu integrable

二、专业英文论文原文

New technique of the computer network

Abstract

The 21 century is an ages of the information economy, being the computer network technique of representative techniques this ages, will be at very fast speed develop soon in continuously creatively, and will go deep into the people's work, life and study. Therefore, control this technique and then seem to be more to deliver the importance. Now I mainly introduce the new technique of a few networks in actuality live of application.

1. Foreword

Internet turns 36, still a work in progress

Thirty-six years after computer scientists at UCLA linked two bulky computers using a 15-foot gray cable, testing a new way for exchanging data over networks, what would ultimately become the Internet remains a work in progress.

University researchers are experimenting with ways to increase its capacity and speed. Programmers are trying to imbue Web pages with intelligence. And work is underway to re-engineer the network to reduce Spam (junk mail) and security troubles.

All the while threats loom: Critics warn that commercial, legal and political pressures could hinder the types of innovations that made the Internet what it is today.

Stephen Crocker and Vinton Cerf were among the graduate students who joined UCLA professor Len Klein rock in an engineering lab on Sept. 2, 1969, as bits of meaningless test data flowed silently between the two computers. By January, three other "nodes" joined the fledgling network.

Then came e-mail a few years later, a core communications protocol called TCP/IP in the late 70s, the domain name system in the 80s and the World

Wide Web - now the second most popular application behind e-mail - in 1990. The Internet expanded beyond its initial military and educational domain into businesses and homes around the world.

Today, Crocker continues work on the Internet, designing better tools for collaboration. And as security chairman for the Internet's key oversight body, he is trying to defend the core addressing system from outside threats.

He acknowledges the Internet he helped build is far from finished, and changes are in store to meet growing demands for multimedia. Network providers now make only "best efforts" at delivering data packets, and Crocker said better guarantees are needed to prevent the skips and stutters now common with video.

Cerf, now at MCI Inc., said he wished he could have designed the Internet with security built-in. Microsoft Corp.Yahoo Inc. and America Online Inc., among others, are currently trying to retrofit the network so e-mail senders can be authenticated - a way to cut down on junk messages sent using spoofed addresses.

Many features being developed today wouldn't have been possible at birth given the slower computing speeds and narrower Internet pipes, or bandwidth, Cerf said.

2.Digital Certificates

Digital certificates are data files used to establish the identity of people and electronic assets on the Internet. They allow for secure, encrypted online communication and are often used to protect online transactions.

Digital certificates are issued by a trusted third party known as a certification authority (CA). The CA validates the identity of a certificate holder and ?signs? the certificate to attest that it hasn’t been forged or altered in any way.

New Uses For Digital Certificates

Digital certificates are now being used to provide security and validation for wireless connections, and hardware manufacturers are one of the latest groups to use them. Not long ago, Version Inc. announced its Cable Modem Authentication Services, which allow hardware manufacturers to embed digital certificates into cable modems to help prevent the pirating of broadband services through device cloning.

Using Version software, hardware makers can generate cryptographic keys and corresponding digital certificates those manufacturers or cable service providers can use to automatically identify individual modems.

This ‘ast-mile’authentication not only protects the value of existing content and services but also positions cable system operators to bring a broad new range of content, applications and value-added services to market.

When a CA digitally signs a certificate, its owner can use it as an electronic passport to prove his identity. It can be presented to Web sites, networks or individuals that require secure access.

Identifying information embedded in the certificate includes the holder’ s name and e-mail address, the name of the CA, a serial number and any activation or expiration data for the certificate. When the CA verifies a user’s identity, the certificate uses the holder’s public encry ption key to protect this data。

Certificates that a Web server uses to confirm the authenticity of a Web site for a user’s browser also employ public keys. When a user wants to send confidential information to a Web server, such as a credit-card number for an online transaction, the browser will access the public key in the server’s digital certificate to verify its identity.

Role of Public-Key Cryptography

The public key is one half of a pair of keys used in public-key cryptography, which provides the foundation for digital certificates.

Public-key cryptography uses matched public and private keys for encryption and decryption. These keys have a numerical value that’s used

by an algorithm to scramble information and make it readable only to users with the corresponding decryption key.

Others to encrypt information meant only for that person use a person’s public key. When he receives the information, he uses his corresponding private key, which is kept secret, to decrypt the data. A person's public key can be distributed without damaging the private key. A Web server using a digital certificate can use its private key to make sure that only it can decrypt confidential information sent to it over the Internet.

The Web server’s certificate is validated by a self-signed CA certificate that identifies the issuing CA. CA certificates are preinstalled on most major Web browsers, including Microsoft Internet Explorer and Netscape Navigator.

The CA certificate tells users whether they can trust the Web server certificate when it’s presented t o the browser. If the validity of the Web server certificate is affirmed, the certificate’s public key is used to secure information for the server using Secure Sockets Layer (SSL) technology.

Digital certificates are used by the SSL security protocol to create a secure ?pipe? between two parties that seek confidential communication. SSL is used in most major Web browsers and commercial Web servers.

3. Digital Wallets

----A digital wallet is software that enables users to pay for goods on the Web .It holds credit-card numbers and other personal information such as a shipping address .Once entered,the data automatically populates order fields at merchant sites .

----When using a digital wallet,consumers don’t need to fill out order forms on each site when they purchase an item because the information has already been stored and is automatically updated and entered into the order fields across merchant sites .Consumers also benefit when using digital wallets because their information is encrypted or protected by a private software code .And merchants benefit by receiving protection against fraud .

----Digital wallets are available to consumers free of charge,and they’re fairly easy to obtain .For example,when a consumer makes a purchase at a merchant site th at’s set up to handle server-side digital wallets,he types his name and payment and shipping information into the merchant’s own form .At the end of the purchase,one consumer is asked to sign up for a wallet of his choice by entering a user name and password for future purchases .Users can also acquire wallets at a wallet vendor’s site .

----Although a wallet is free for consumers,vendors charge merchants for wallets .

----Digital wallets come in two main types: client-side and server- side .Within those divisions are wallets that work only on specific merchant sites and those that are merchant agnostic .

----Client-based digital wallets,the older of the two types,are falling by the wayside,according to analysts,because they require users to download and install software .A user downloads the wallet application and inputs payment and mailing information .At that point,the information is secured and encrypted on the user’s hard drive .The user retains control of his credit card and personal information locally .

----With a server-based wallet,a user fills out his personal information,and a cookie is automatically downloaded .(A cookie is a text file that contains information about the user .)In this scenario,the consumer information resides on the server of a financial institution or a digital wallet vendor rather than on the user’s PC .

----Server-side wallets provide assurance against merchant fraud because they use certificates to verify the identity of all parties .When a party makes a transaction,it presents its certificate to the other parties involved .A certificate is an attachment to an electronic message used to verify the identity of the party and to provide the receiver with the means to encode a reply .

----Furthermore,the cardholder’s sensitiv e data is typically housed at a financial institution,so there’s an extra sense of security because financial environments generally provide the highest degree of security .

----But even though wallets provide easy shopping online, adoption hasn’t been wi despread。

----Standards are pivotal to the success of digital wallets .

----Last month,major vendors,including Microsoft Corp .,Sun Microsystems Inc .and America Online Inc .announced their endorsement of a new standard called EMCL,or E-Commerce Modeling Language,to give Web merchants a standardized way to collect electronic data for shipping,billing and payment .

4. Grid Storage

Definition: Grid storage, analogous to grid computing, is a new model for deploying and managing storage distributed across multiple systems and networks, making efficient use of available storage capacity without requiring a large, centralized switching system.

A grid is, in fact, a meshed network in which no single centralized switch or hub controls routing. Grids offer almost unlimited scalability in size and performance because they aren’t constrained by the need for ever-larger central switches. Grid networks thus reduce component costs and produce a reliable and resilient structure.

Applying the grid concept to a computer network lets us harness available but unused resources by dynamically allocating and deal locating capacity, bandwidth and processing among numerous distributed computers. A computing grid can span locations, organizations, machine architectures and software boundaries, offering power, collaboration and information access to connected users. Universities and research facilities are using grids to build what amounts to supercomputer capability from PCs, Macintoshes and Linux boxes.

After grid computing came into being, it was only a matter of time before a similar model would emerge for making use of distributed data storage. Most storage networks are built in star configurations, where all servers and storage devices are connected to a single central switch. In contrast, grid topology is built with a network of interconnected smaller switches that can scale as bandwidth increases and continue to deliver improved reliability and higher performance and connectivity.

Based on current and proposed products, it appears that a grid storage system should include the following:

Modular storage arrays: These systems are connected across a storage network using serial ATA disks. The systems can be block-oriented storage arrays or network-attached storage gateways and servers.

Common virtualization layer: Storage must be organized as a single logical pool of resources available to users.

Data redundancy and availability: Multiple copies of data should exist across nodes in the grid, creating redundant data access and availability in case of a component failure.

Common management: A single level of management across all nodes should cover the areas of data security, mobility and migration, capacity on demand, and provisioning.

Simplified platform/management architecture: Because common management is so important, the tasks involved in administration should be organized in modular fashion, allowing the auto discovery of new nodes in the grid and automating volume and file management.

Three Basic Benefits

Applying grid topology to a storage network provides several benefits, including the following:

Reliability. A well-designed grid network is extremely resilient. Rather than providing just two paths between any two nodes, the grid offers multiple paths between each storage node. This makes it easy to service and replace components in case of failure, with minimal impact on system availability or downtime.

Performance. The same factors that lead to reliability also can improve performance. Not requiring a centralized switch with many ports eliminates a potential performance bottleneck, and applying load-balancing techniques to the multiple paths available offers consistent performance for the entire network.

Scalability. It’s easy to expand a grid network using inexpe nsive switches with low port counts to accommodate additional servers for increased performance, bandwidth and capacity. In essence, grid storage is a way to scale out rather than up, using relatively inexpensive storage building blocks.

三、专业中文论文原文

关于提高信息与计算科学专业的就业竞争力的对策探讨

一、影响信息与计算科学专业就业竞争力的原因浅析

1.从专业的发展的现状来看

信息与计算科学是由信息科学、计算科学和运筹学与控制科学等学科交叉渗透而形成的一个新的专业。迄今为止,全国已有近500所高校开设了信息与计算科学专业,但相当多的院校存在着办学经验不足,师资力量匮乏,以及办学条件、教材等诸多因素的影响,在培养学生的过程中出现了这样或那样的问题。

首先,专业定位不明确。由于该专业是由老的计算数学或应用数学专业改造而成,因而存在照搬旧专业培养模式的现象,很多学校要么是以计算数学及其应用软件为发展方向,要么是以计算机科学作为发展方向,无法适应当前经济发展对人才的培养要求及就业市场的需求。

其次,课程体系混乱。由于专业定位不明确,因而造成了课程体系混乱,有的是开的计算数学的专业课程体系,有的则完全按照计算机专业的课程课程体系开设,更有的是开设一部分数学,一部分计算机,一部分管理课程,造成该专业看似是“什么行业都能胜任”的万金油,实则是“蜻蜓点水”,影响学生的就业。

再者,实践教学环节不完善。目前,信息与计算科学专业学生的实践教学环节仍然比较薄弱,这一点主要体现在如下两点。

(1)理论多,实践少。以理论教学为主,实践教学则只作为理论教学的一个论证环节和补充而被摆在了次要地位。造成学生抱怨所学课程过于枯燥,没有实际应用,学习的积极性也不高。只有书本的知识,没有实际的应用经历,严重影响了学生的就业。当前如“ 雨后春笋”般呈现的各种IT技能培训班,能在几个月甚至更短的时间里帮助学生掌握一定的专业技能从而实现顺利就业,靠的就是强化的实践,这很值得高校的思考与借鉴。

(2)没有建立固定的校外实习基地供学生完成课程实践以及毕业设计环节,只有一部分毕业生在最后一个学期分散到一些企业去实习,这在一定程度上影响到了实践活动的质量和综合能力培养。

2. 从毕业生自身来看首先,缺少职业规划。职业规划是大学生迈入社会的第一个规划,职业指导专家施华锋说,职业规划是大学生进入社会前应做的关键工作。没有职业规划,人生没有方向,做好这个规划有助于帮助大学生清晰定位。如果不做好职业规划,人生就会没有方向。大学生在求职时,应该尽量客观地审视自己,充分分析自己的专业、兴趣、爱好、特长等,找到真正适合自己的职业。

再者,对于大学生职业发展而言,自己唯一可控的就是自己的就业能力。对个人而言,就业能力包括专业能力与市场能力两个部分。专业能力取决于他们所拥有的知识、技能与态度等资产以及他们使用和配置这些资产的方式,而市场能力取决于他们向雇主展示这些资产的方式以及他们寻找工作的特定环境,特别是所面临的劳动力市场环境。在专业能力方面,以敬业精神、职业道德和职业操守为代表的态度型资产是大学生专业能力中的关键,以解决问题能力为代表的知识技能型资产是专业能力的基石。在市场能力方面,为寻找更好的职业发展机会,大学生必须要了解现在整个劳动力市场,特别是大学生的劳动力市场的总体供求数量信息和结构信息,要了解职位具体的职责要求,要了解自己个人就业能力的水平,同时还必须改进自己的展示能力。所谓展示的能力最核心的问题就是大学生如何把自身的各种资本、能力的信息传递给市场,让市场明白自己的价值。如何把自己所拥有的专业能力通过自己的语言或者测试的方式表达给市场。

3.从社会来看

首先,社会经济发展的程度和速度始终是就业市场兴旺发达的生命线。社会需求量大的专业,学生会对照用人单位的标准,不断完善自己。相反,学生会陷入无目标的迷茫状态。信息与计算科学是新兴的边缘学科,社会普通认可程度不高。甚至不少用人单位把“信息与计算科学”等同于“计算机科学与技术”。从各类招聘会以及网上招聘会对专业需求的数据来看,指定要信息与计算科学专业毕业生的单位微乎其微。甚至报考国家公务员几乎通不过专业审查。这些社会现象严重打击学生的学习热情。越是工作找不到,越是不愿意学习;越是不好好学习,工作越是找不到。长此以往,必然会陷入恶性循环的怪圈。

4.从学校来看

首先,学校在某一领域内学术研究水平集中体现了该领域学生的专业竞争力。企业在挑选人才的时候,往往会优先考虑在本领域社会影响力大的学校。譬如:浙江理工大学的服装、纺织这两个专业拥有悠久的历史、深厚的专业积淀、广泛的校企联合。因而,这些毕业生供不应求。相反,信息与计算科学是新兴学科,处于发展期。教师在该领域的研究尚且刚刚起步,更别提成果了,这在一定程度上增加了学生择业的困惑,影响了就业竞争力。

其次,高校的就业指导质量高低同样也影响就业竞争力。就业指导人员的工作态度、工作方式、工作成效等对就业竞争力的影响很大。就业指导人员坚持“就业指导四年一贯制”的原则,促使学生树立“先就业,后择业”的观念,准确定位,有效规划,就能使学生在职场立于不败之地。反之亦然。

二、提高信息与计算科学专业就业竞争力的对策

1.“宽口径、有侧重”,着力构建提升毕业生就业竞争力的长效机制

信息与计算科学涵盖面很广,灵活度大。但是在专业方向选择和课程的开设上应有侧重点,不能“面面俱到”。

首先,信息与计算科学的人才培养应该遵循“强基础、宽口径、重实际”的办学指导思想。“强基础”指深厚的数学基础不能削弱,这是与计算机专业、通信工程专业和信息与管理专业的最大区别。培养学生建立数学模型和模型实现的能力。关于这一点,可以通过参加国家的数学建模大赛,提高学生的学习积极性,培养用数学思维解决实际问题。“宽口径”指基于本科教育的特点,加强与其他学科的渗透,尤其是与管理类、计算机类的交叉。“重实际”指在教学中,教师应该联系实际,培养学生的动手能力。

其次,根据目前信息与计算科学毕业生供职的行业来看今后该专业可以朝三个方向发展:侧重于信息科学方向、侧重于计算科学方向、侧重于经济管理方向。至于侧重于哪个方向,完全由高校的软、硬件条件决定。

再者,现代社会是个信息化的社会,知识的更新是日新月异,课程的设计不是一成不变的,应该根据社会的需求可适当的开设一些与社会接轨的课程。

2.增强信息与计算科学的实践环节

信息与计算科学专业本身的实践性极强。在学科发展、专业建设以及教学环节当中都应当紧密联系信息技术与计算技术的实际,特别是学科最新发展与高新技术的实际,加强学生的数学建模、数学软件应用、计算机编程等实践能力的培养。信息与计算科学专业的实践环节可由数学实验、课程设计环节构成。

首先,数学类实验。数学类课程有:数学分析、高等代数、空间解析几何、常微分方程、离散数学、复变函数与积分变换、数值分析、运筹学、数据分析。概率论与数理统计、数值分析、运筹学、数据分析都可以开设相应的实验课程,其目的:一是通过实验课, 掌握常用的数学软件( 如Matlab、SAS 等) 的使用, 加深对相关数学概念的理解。二是训练学生用数学工具解决实际问题的能力。三是以相应的数学问题为背景,要求学生自己编写程序,训练学生的算法设计与编程能力。

四、Mathematica软件介绍

Mathematica是一款科学计算软件,很好地结合了数值和符号计算引擎、图形系统、编程语言、文本系统、和与其他应用程序的高级连接。很多功能在相应领域内处于世界领先地位,截至2009年,它也是为止使用最广泛的数学软件之一。Mathematica的发布标志着现代科技计算的开始。自从20世纪60年代以来,在数值、代数、图形、和其它方面应用广泛,Mathematica是世界上通用计算系统中最强大的系统。自从1988发布以来,它已经对如何在科技和其它领域运用计算机产生了深刻的影响。

目录

Mathematica的历史

人们常说,Mathematica的发布标志着现代科技计算的开始。自从上世纪六十年代以来,在数值、代数、图形、和其它方面一直有个别的软件包存在。但是,Mathematica的基本概念是用一个连贯的和统一的方法创造一个能适用于科技计算各个方面的软件系统。实现这一点的关键之处是发明了一种新的计算机符号语言。这种语言能仅仅用很少量的基本元素制造出广泛的物体,满足科技计算的广泛性。这在人类历史上还是第一次。

当Mathematica1.0版发布时,《纽约时代报》写道:“这个软件的重要性不可忽视”;紧跟着《商业周刊》又将Mathematica评比为当年十大最重要产品。在科技界,Mathematica被形容为智能和实践的革命。

Mathematica的影响

Mathematica 应用广泛

最初,Mathematica的影响主要限于物理学、工程学、和数学领域。但是,随着时间的变化,Mathematica在许多重要领域得到了广泛的应用。现在,它已经被应用于科学的各个领域--物理、生物、社会学、和其它。许多世界顶尖科学家都是它的忠实支持者。它在许多重要的发现中扮演着关键的角色,并是数以千计的科技文章的基石。在工程中,Mathematica已经成为开发和制造的标准。世界上许多重要的新产品在它们的设计某一阶段或其它阶段都依靠了Mathematica的帮助。在商业上,Mathematica在复杂的金融模型中扮演了重要的角色,广泛地应用于规划和分析。同时,Mathematica也被广泛应用于计算机科学和软件发展:它的语言元件被广泛地用于研究、原型、和界面环境。

Mathematica 中文版

Wolfram Research 于2011年3月23日发布了 Mathematica 8.0.1 简体中文版。该版本增加了500多个新函数,功能涵盖更多应用领域,并拥有更友好更高质量的中文用户界面、中文参考资料中心及数以万计的中文互动实例,使中国用户学习和使用 Mathematica 更加方便快捷。

Mathematica的用户群

Mathematica的用户群中最主要的是科技工作者和其它专业人士。但是,Mathematica还被广泛地用于教学中。

ansys与mathematica

数学中的许多计算是非常繁琐的,特别是函数的作图费时又费力,而且所画的图形很不规范,所以现在流行用Methematica符号计算系统进行学习,从高中到研究生院的数以百计的课程都使用它,很多问题便迎刃而解。此外,随着学生版的出现,Mathematica已经在全世界的学生中流行起来,成为了一个著名的工具。

Mathematica的开发工作

Mathematica的开发工作是由世界级的队伍组成的。这支队伍自从成立以来一直由史蒂芬·沃尔夫勒姆领导。Mathematica的成功使得公司能够集中注意力在非常长远的目标上,运行独特的研发项目,以及通过各种各样的免费网站支持世界各地的知识爱好者。

长期以来,Mathematica核心设计的普遍性使得其涉及的领域不断增长。从刚开始是一个主要用于数学和科技计算的系统,到现在发展成许多计算领域的主要力量,Mathematica已经成为世界上最强大的通用计算系统。

Mathematica运算

Mathematica 基本运算

a+ b+c 加

a-b 减

a b c 或 a*b*c 乘

a/b 除

-a 负号

a^b 次方

Mathematica 数字的形式

256 整数

2.56 实数

11/35 分数

2+6I 复数

常用的数学常数

Pi 圆周率,π=3.141592654…

E 尤拉常数,e=2.71828182…

Degree 角度转换弧度的常数,Pi/180

I 虚数,其值为√-1

Infinity 无限大

指定之前计算结果的方法

% 前一个运算结果

%% 前二个运算结果

%%…%(n个%) 前n个运算结果

%n 或 Out[n] 前n个运算结果

复数的运算指令

a+bI 复数

Conjugate[a+bI] 共轭复数

Re[z], Im[z] 复数z的实数/虚数部分

Abs[z] 复数z的大小或模数(Modulus)

Arg[z] 复数z的幅角(Argument)

Mathematica 输出的控制指令

expr1; expr2; expr3 做数个运算,但只印出最后一个运算的结果expr1; expr2; expr3; 做数个运算,但都不印出结果

expr; 做运算,但不印出结果

常用数学函数

Sin[x],Cos[x],Tan[x],Cot[x],Sec[x],Csc[x] 三角函数,其引数的单位为弧度

Sinh[x],Cosh[x],Tanh[x],… 双曲函数

ArcSin[x],ArcCos[x],ArcTan[x] 反三角函数

ArcCot[x],ArcSec[x],ArcCsc[x]

ArcSinh[x],ArcCosh[x],ArcTanh[x],… 反双曲函数

Sqrt[x] 根号

Exp[x] 指数

Log[x] 自然对数

Log[a,x] 以a为底的对数

Abs[x] 绝对值

Round[x] 最接近x的整数

Floor[x] 小于或等于x的最大整数

Ceiling[x] 大于或等于x的最小整数

Mod[a,b] a/b所得的馀数

n! 阶乘

Random[] 0至1之间的随机数(最新版本已经不用这个函数,改为使用RandomReal[])

Max[a,b,c,...],Min[a,b,c,…] a,b,c,…的极大/极小值

数值设定

x=a 将变数x的值设为a

x=y=b 将变数x和y的值均设为b

x=. 或 Clear[x] 除去变数x所存的值

变数使用的一些法则

xy 中间没有空格,视为变数xy

x y x乘上y

3x 3乘上x

x3 变数x3

x^2y 为 x^2 y次方运算子比乘法的运算子有较高的处理顺序

四个常用处理代数的指令

Expand[expr] 将 expr展开

Factor[expr] 将 expr因式分解

Simplify[expr] 将 expr化简成精简的式子

FullSimplify[expr] Mathematica 会尝试更多的化简公式,将 expr 化成更精简的式子

多项式/分式转换的函数

ExpandAll[expr] 把算式全部展开

Together[expr] 将 expr各项通分在并成一项

Apart[expr] 把分式拆开成数项分式的和

Apart[expr,var] 视var以外的变数为常数,将 expr拆成数项的和Cancel[expr] 把分子和分母共同的因子消去

分母/分子的运算

Denominator[expr] 取出expr的分母

Numerator[expr] 取出expr的分子

ExpandDenominator[expr] 展开expr的分母

ExpandNumerator[expr] 展开expr的分子

多项式的另二种转换函数

Collect[expr,x] 将 expr表示成x的多项式,

Collect[expr,{x,y,…}] 将 expr分别表示成x,y,…的多项式

FactorTerms[expr] 将 expr的数值因子提出,

如 4x+2=2(2x+1)

FactorTerms[expr,x] 将 expr中把所有不包含x项的因子提出

FactorTerms[expr,{x,y,…}] 将 expr中把所有不包含{x,y,...}项的因子提出

三角函数、双曲函数和指数的运算

TrigExpand[expr] 将三角函数展开

TrigFactor[expr] 将三角函数所组成的数学式因式分解

TrigReduce[expr] 将相乘或次方的三角函数化成一次方的基本三角函数之组合

ExpToTrig[expr] 将指数函数化成三角函数或双曲函数

TrigToExp[expr] 将三角函数或双曲函数化成指数函数

复数、次方乘积之展开

ComplexExpand[expr] 假设所有的变数都是实数来对 expr展开

ComplexExpand[expr,{x,y,…}] 假设x,y,..等变数均为复数来对expr展开

PowerExpand[expr] 将

多项式项次、系数与最高次方之取得

Coefficient[expr,form] 于 expr中form的系数

Exponent[expr,form] 于 expr中form的最高次方

Part[expr,n] 或 expr[[n]] 在 expr项中第n个项

代换运算子

expr/.x->value 将 expr里所有的x均代换成value

expr/.{x->value1,y->value2,…} 执行数个不同变数的代换

expr/.{{x->value1},{x->value2},…} 将 expr代入不同的x值

expr//.{x->value1,y->value2,…} 重复代换到 expr不再改变为止求

解方程式的根

Solve[lhs==rhs,x] 解方程式lhs==rhs,求x

Nsolve[lhs==rhs,x] 解方程式lhs==rhs的数值解

Solve[{lhs1==rhs1,lhs2==rhs2,…},{x,y,…}] 解联立方程式,求x,y,…

NSolve[{lh s1==rhs1,lhs2==rhs2,…},{x,y,…}] 解联立方程式的数值解

FindRoot[lhs==rhs,{x,x0}] 由初始点x0求lhs==rhs的根

Mathematica 的四种括号

(term) 圆括号,括号内的term先计算

f[x] 方括号,内放函数的引数

{x,y,z} 大括号或串列括号,内放串列的元素

p[[i ]] 或 Part[p,i] 双方括号,p的第i项元素

p[[i,j]] 或 Part[p,i,j] p的第i项第j个元素

缩短Mathematica输出的指令

expr//Short 显示一行的计算结果

Short[expr,n] 显示n行的计算结果

Command; 执行command,但不列出结果

查询Mathematica的物件

?Command 查询Command的语法及说明

??Command 查询Command的语法和属性及选择项

?Aaaa* 查询所有开头为Aaaa的物件

函数的定义、查询与清除

f[x_]= expr 立即定义函数f[x]

f[x_]:= expr 延迟定义函数f[x]

f[x_,y_,…] 函数f有两个以上的引数

?f 查询函数f的定义

Clear[f] 或 f=. 清除f的定义

Remove[f] 将f自系统中清除掉

含有预设值的Pattern

a_+b_. b的预设值为0,即若b从缺,则b以0代替

x_ y_ y的预设值为1

x_^y_ y的预设值为1

条件式的自订函数

lhs:=rhs/;condition 当condition成立时,lhs才会定义成rhs

If指令

If[test,then,else] 若test为真,则回应then,否则回应else If[test,then,else,unknow] 同上,若test无法判定真或假时,则回应unknow

极限

Limit[expr,x->c] 当x趋近c时,求expr的极限

Limit[expr,x->c,Direction->1]

Limit[expr,x->c,Direction->-1]

微分

D[f,x] 函数f对x作微分

D[f,x1,x2,…] 函数f对x1,x2,…作微分

D[f,{x,n}] 函数f对x微分n次

D[f,x,NonConstants->{y,z,…}] 函数f对x作微分,将y,z,…视为x的函数

全微分

Dt[f] 全微分df

Dt[f,x] 全微分

Dt[f,x1,x2,…] 全微分

Dt[f,x,Constants->{c1,c2,…}] 全微分,视c1,c2,…为常数

不定积分

Integrate[f,x] 不定积分∫f dx

定积分

Integrate[f,{x,xmin,xmax}] 定积分

Integrate[f,{x,xmin,xmax},{y,ymin,ymax}] 定积分

列之和与积

Sum[f,{i,imin,imax}] 求和

Sum[f,{i,imin,imax,di}] 求数列和,引数i以di递增

Sum[f,{i,imin,imax},{j,jmin,jmax}]

Product[f,{i,imin,imax}] 求积

Product[f,{i,imin,imax,di}] 求数列之积,引数i以di递增

Product[f,{i,imin,imax},{j,jmin,jmax}]

函数之泰勒展开式

Series[expr,{x,x0,n}] 对 expr于x0点作泰勒级数展开至(x-x0)n 项

Series[expr,{x,x0,m},{y,y0,n}] 对x0和y0展开

关系运算子

a==b 等于

a>b 大于

a>=b 大于等于

a

a<=b 小于等于

a!=b 不等于

逻辑运算子

!p not

p||q||… or

p&&q&&… and

Xor[p,q,…] exclusive or

LogicalExpand[expr] 将逻辑表示式展开

基本二维绘图指令

Plot[f,{x,xmin,xmax}]

画出f在xmin到xmax之间的图形

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