應(yīng)用物理微積分畢業(yè)論文中英文資料對(duì)照外文翻譯文獻(xiàn)綜述70講述

1、應(yīng)用物理微積分畢業(yè)論文中英文資料對(duì)照外文翻譯文獻(xiàn)綜述70應(yīng)用物理微積分；中英文資料對(duì)照外文翻譯文獻(xiàn)綜述；牛頓與萊布尼茲創(chuàng)立微積分之解析；摘要:文章主要探討了牛頓和萊布尼茲所處的時(shí)代背景；關(guān)鍵詞:牛頓;萊布尼茲;微積分;哲學(xué)思想；Abstract:Thispapermainly；Keywords:Newton;Leibniz;；今天,微積分已成為根本的數(shù)學(xué)工具而被廣泛地應(yīng)用于；一、牛頓所處的時(shí)代背景及其哲學(xué)思想；“應(yīng)用物理微積分中英文資料對(duì)照外文翻譯文獻(xiàn)綜述牛頓與萊布尼茲創(chuàng)立微積分之解析摘 要:文章主要探討了牛頓和萊布尼茲所處的時(shí)代背景以及他們的哲學(xué)思想對(duì)其創(chuàng)立廣泛地應(yīng)用于自然科學(xué)的各個(gè)領(lǐng)域的根

2、本數(shù)學(xué)工具微積分的影響。關(guān)鍵詞:牛頓;萊布尼茲;微積分;哲學(xué)思想Abstract: This paper mainly discusses the background of the times of Newton and Leibniz, and their philosophy of its founder is widely used in various fields of natural science basic mathematical tools - calculus.Key words: Newton; Leibniz; calculus; philosophical tho

3、ught今天,微積分已成為根本的數(shù)學(xué)工具而被廣泛地應(yīng)用于自然科學(xué)的各個(gè)領(lǐng)域。恩格斯說(shuō)過(guò):“在一切理論成就中,未有象十七世紀(jì)下半葉微積分的創(chuàng)造那樣被看作人類精神的最高勝利了,如果在某個(gè)地方我們看到人類精神的純粹的和唯一的功績(jī),那就正是在這里。1 (p. 244) 本文試從牛頓、萊布尼茲創(chuàng)立“被看作人類精神的最高勝利的微積分的時(shí)代背景及哲學(xué)思想對(duì)其展開(kāi)剖析。一、牛頓所處的時(shí)代背景及其哲學(xué)思想“牛頓( Isaac Newton ,1642 - 1727) 1642 年生于英格蘭。?,1661 年,入英國(guó)劍橋大學(xué),1665 年,倫敦流行鼠疫,牛頓回到鄉(xiāng)間,終日思考各種問(wèn)題,運(yùn)用他的智慧和數(shù)年來(lái)獲得的知

4、識(shí),創(chuàng)造了流數(shù)術(shù)(微積分) 、萬(wàn)有引力和光的分析。2 (p. 155)1665 年5 月20 日,牛頓的手稿中開(kāi)始有“流數(shù)術(shù)的記載。?流數(shù)的介紹?和?用運(yùn)動(dòng)解決問(wèn)題?等論文中介紹了流數(shù)(微分) 和積分,以及解流數(shù)方程的方法與積分表。1669 年,牛頓在他的朋友中散發(fā)了題為?運(yùn)用無(wú)窮多項(xiàng)方程的分析學(xué)?的小冊(cè)子,在這里,牛頓不僅給出了求一個(gè)變量對(duì)于另一個(gè)變量的瞬時(shí)變化率的普遍方法,而且證明了面積可以由求變化率的逆過(guò)程得到。因?yàn)槊娣e也是用無(wú)窮小面積的和來(lái)表示從而獲得的。所以牛頓證明了這樣的和能由求變化率的逆過(guò)程得到(更精確地說(shuō),和的極限能夠由反微分得到) ,這個(gè)事實(shí)就是我們現(xiàn)在所講的微積分根本定理。

5、這里“, 牛頓使用的是無(wú)窮小方法,把變量的無(wú)限小增量叫做“瞬,瞬是無(wú)窮小量,是不可分量, 或是微元, 牛頓通過(guò)舍棄“瞬求得變化率。3 (p. 199) 1671 年牛頓將他關(guān)于微積分研究的成果整理成?流數(shù)法和無(wú)窮級(jí)數(shù)?(1736) ,在這里,他認(rèn)為變量是連續(xù)運(yùn)動(dòng)產(chǎn)生的,他把變量叫做流,變量的變化率叫做流數(shù)。牛頓更清楚地陳述了微積分的根本問(wèn)題:兩個(gè)流之間的關(guān)系,求它們流數(shù)之間的關(guān)系,以及它的逆問(wèn)題。?流數(shù)法和無(wú)窮級(jí)數(shù)?是一部較完整的微積分著作。書(shū)的后半局部通過(guò)20 個(gè)問(wèn)題廣泛地介紹了流數(shù)法各無(wú)窮級(jí)數(shù)的應(yīng)用。1676 年,牛頓寫(xiě)出了?求曲邊形的面積?(1704) ,在這里,牛頓的微積分思想發(fā)生了重

6、大變化,他放棄了微元或無(wú)窮小量,而采用了最初比和最后比的方法。 1687 年牛頓發(fā)表了它的劃時(shí)代的科學(xué)名著?自然哲學(xué)的數(shù)學(xué)原理?,流數(shù)術(shù)(即微積分) 是其三大發(fā)現(xiàn)之一。正如愛(ài)因斯坦所說(shuō)的:“牛頓啊?你所發(fā)現(xiàn)的道路在你的那個(gè)時(shí)代是一位具有最高思維能力和創(chuàng)造能力的人所發(fā)現(xiàn)的唯一道路,你所創(chuàng)造的概念即使在今天仍然指導(dǎo)著我們的物理學(xué)思想。4 (p. 192)牛頓生活的時(shí)代正是英國(guó)發(fā)生變化的時(shí)代,當(dāng)時(shí)英國(guó)發(fā)生了國(guó)內(nèi)戰(zhàn)爭(zhēng),資產(chǎn)階級(jí)和貴族的階級(jí)妥協(xié),使英國(guó)資產(chǎn)階級(jí)革命明顯的帶上了不徹底性。當(dāng)時(shí)的英國(guó)資產(chǎn)階級(jí)正在為現(xiàn)存的剝削階級(jí)的一切上層建筑做永恒存在的論證,因此絕對(duì)化的思想成為占統(tǒng)治地位的主導(dǎo)思想,它也影響

7、到當(dāng)時(shí)的自然科學(xué)家們把形而上學(xué)的思想方法絕對(duì)化。牛頓的思想也受到了英國(guó)資產(chǎn)階級(jí)革命不徹底性的影響,因而牛頓也往往不能從自然界本身或事物的本身來(lái)尋找最初的原因,而借助于外來(lái)的推動(dòng)力。 牛頓在30 歲以前發(fā)現(xiàn)了微積分,并建立了經(jīng)典力學(xué)體系,而他的后半生在自然科學(xué)的研究上幾乎一事無(wú)成。這是由于在資本主義產(chǎn)生和形成的時(shí)期,資產(chǎn)階級(jí)曾經(jīng)向宗教神學(xué)發(fā)起沖擊,幫助科學(xué)從神學(xué)中解放出來(lái)。但是當(dāng)資產(chǎn)階級(jí)的地位穩(wěn)固以后,階級(jí)斗爭(zhēng)逐漸激化之時(shí),資產(chǎn)階級(jí)就逐漸衰退,他們就抓住各種各樣的宗教信念作為奴役人民的思想武器。牛頓受其影響很大,其前半生由于自發(fā)的唯物主義的思想傾向,使他獲得了巨大成就,而后半生那么完全沉迷于神學(xué)

8、的研究。牛頓繼承了培根的經(jīng)驗(yàn)主義傳統(tǒng),特別重視實(shí)驗(yàn)和歸納推理的作用,他曾斷言,自然科學(xué)只能從經(jīng)驗(yàn)事實(shí)出發(fā)解釋世界。這在當(dāng)時(shí)對(duì)打擊經(jīng)院哲學(xué)的崇尚空談、妄稱神意來(lái)歪曲自然界是起過(guò)積極作用的。但是“, 牛頓卻拘泥于經(jīng)驗(yàn)事實(shí),片面強(qiáng)調(diào)歸納的重要性。只有大量的感性材料,一切停留在事物的現(xiàn)象上,單獨(dú)依靠歸納的方法是得不出系統(tǒng)的普遍性的理性認(rèn)識(shí)來(lái)的。在分析和綜合、演繹和歸納的問(wèn)題上,形而上學(xué)使牛頓陷入了矛盾。5 (p. 123)二、萊布尼茲所處的時(shí)代背景及其哲學(xué)思想“萊布尼茲(Gottfried Wilhelm Leibniz ,1646 - 1716)生于德國(guó)。?,1672 年赴巴黎,在那里接觸到惠更斯等

9、一些數(shù)學(xué)名流,引其進(jìn)入了數(shù)學(xué)領(lǐng)域,開(kāi)始微積分的創(chuàng)造性工作。2 (p. 165)1684 年萊布尼茨發(fā)表了數(shù)學(xué)史上第一篇正式的微積分文獻(xiàn)?一種求極限值和切線的新方法?。這篇文獻(xiàn)是他自1673 年以來(lái)的微積分研究的概括與成果,其中定義了微分,廣泛地采用了微分符號(hào)dx、dy ,還給出了和、差、積、商及乘冪的微分法那么。同時(shí)包括了微分法在求切線、極大、極小值及拐點(diǎn)方面的應(yīng)用。兩年后,又發(fā)表了一篇積分學(xué)論文?深?yuàn)W的幾何與不變量及其無(wú)限的分析?,其中首次使用積分符號(hào)“,初步論述了積分(或求積) 問(wèn)題與微分求切線問(wèn)題的互逆問(wèn)題。即今天大家熟知的牛頓- 萊布尼茨公式ba f ( x) dx = f ( b)

10、- f ( a) ,為我們勾畫(huà)了微積分學(xué)的根本雛形和開(kāi)展藍(lán)圖?！芭ｎD建立微積分是從運(yùn)動(dòng)學(xué)的觀點(diǎn)出發(fā),而萊布尼茲那么從幾何學(xué)的角度去考慮,所創(chuàng)設(shè)的微積分符號(hào)遠(yuǎn)遠(yuǎn)優(yōu)于牛頓符號(hào),并有效地促進(jìn)了微積分學(xué)的開(kāi)展。6 (p. 120) 牛頓發(fā)現(xiàn)微積分(1665 - 1666 年) 比萊布尼茨至少早了9 年,然而萊布尼茨公開(kāi)發(fā)表它的微積分文章比牛頓早3 年。據(jù)萊布尼茨本人提供的證據(jù)說(shuō)明他是在1674 年形成了微分的思想與方法。如果說(shuō),牛頓建立微積分主要是從運(yùn)動(dòng)學(xué)的觀點(diǎn)出發(fā),而萊布尼茲那么是從哲學(xué)的和幾何學(xué)的角度去考慮,特別是和巴羅的“微分三角形有密切關(guān)系,萊布尼茲稱它為“特征三角形。巴羅的微分三角形對(duì)萊布尼

11、茲有著重要啟發(fā),對(duì)微分三角形的研究,使他意識(shí)到求切線和求積問(wèn)題是一對(duì)互逆的問(wèn)題。萊布尼茲第一個(gè)表達(dá)出微分和積分之間的互逆關(guān)系。 萊布尼茲的許多研究成果和思想的開(kāi)展,都包含在從1673 年起寫(xiě)的但從未發(fā)表過(guò)的成百頁(yè)的筆記中。1673 年左右,他看到求曲線的切線的正問(wèn)題和反問(wèn)題的重要性,他完全相信反方法等價(jià)于通過(guò)求和來(lái)求面積和體積。1684 年,萊布尼茲發(fā)表第一篇微分學(xué)論文?一種求極大、極小和切線的新方法,它也適用于分式或無(wú)理量,以及這種新方法的奇妙類型的計(jì)算?,對(duì)他以往的研究作了初步整理,表達(dá)了微分學(xué)的根本原理,認(rèn)為函數(shù)的無(wú)限小增量是自變量無(wú)限小變化的結(jié)果,且把這個(gè)函數(shù)的增量叫做微分,用字母d表

12、示。1675 - 1676 年間,他從求曲邊形面積出發(fā)得到積分的概念, 給出微積分根本定理baf ( x) dx = f ( b)- f ( a) 。1686 年萊布尼茲發(fā)表積分學(xué)論文?潛在的幾何與分析不可分和無(wú)限?。1693 年,他給出了上述定理的一個(gè)證明。以上這些都發(fā)表在?教師學(xué)報(bào)?上。將微分和積分統(tǒng)一起來(lái),是微積分理論得以建立的一個(gè)重要標(biāo)志。萊布尼茲出生在德國(guó)路德派諸侯與天主教諸侯之間的對(duì)立而引起的“三十年戰(zhàn)爭(zhēng)結(jié)束前。為了改變宗教紛爭(zhēng)的局面,萊布尼茲立志要發(fā)現(xiàn)一種新的天主教和路德教都能適合的關(guān)于實(shí)體的學(xué)說(shuō),以成為兩派教會(huì)得以聯(lián)合的哲學(xué)根底。雖然萊布尼茲的意圖是不可能實(shí)現(xiàn)的,但他后來(lái)卻因此

13、提出了一種與笛卡爾不同的實(shí)體學(xué)說(shuō)單子論。“單子論是萊布尼茲哲學(xué)的核心內(nèi)容。萊布尼茲認(rèn)為一切事物都由單子這種精神的實(shí)體構(gòu)成的,這種單子既非物質(zhì)的而又具有一定的質(zhì),它是精神性的,萊布尼茲就把它比之于靈魂。只有精神的單子才是真實(shí)的存在的實(shí)體,從單子是不可分的,即沒(méi)有局部的“單純實(shí)體這一點(diǎn)出發(fā),萊布尼茲就推論出它的一系列特征:單子沒(méi)有局部,它就不能以自然的方式通過(guò)各局部的組合而產(chǎn)生,或通過(guò)各局部的分解而消滅,因此它的生滅只能出于上帝的突然創(chuàng)造或消滅;單子沒(méi)有局部,就不能設(shè)想有什么東西可以進(jìn)入其內(nèi)部來(lái)造成變化,這樣,單子就成了各自獨(dú)立或徹底孤立的東西,各單子之間不能有任何真正的相互作用或影響。單子之間沒(méi)

14、有量的差異, 而只有質(zhì)的不同。7 (p. 85)總之,萊布尼茲的根本觀點(diǎn)是唯心主義的,也是形而上學(xué)的。他把宇宙的秩序都?xì)w因于上帝的預(yù)先決定。他肯定許多必然真理并非來(lái)自經(jīng)驗(yàn),他認(rèn)為不但認(rèn)識(shí)的對(duì)象都是由精神性的“單子所構(gòu)成。而且認(rèn)識(shí)的主體也只能作為精神實(shí)體的心靈這種“單子。他把一切開(kāi)展變化都?xì)w因于上帝的“前定,實(shí)際也就否認(rèn)了真正的開(kāi)展,這是他的觀點(diǎn)的消極的一面。但另一方面,萊布尼茲的哲學(xué)也有積極方面,它的哲學(xué)中含有豐富的辯證法思想,他肯定實(shí)體本身就具有力,因而是能動(dòng)的,實(shí)質(zhì)上肯定了物質(zhì)與運(yùn)動(dòng)不可分的思想,他試圖解決“不可分的點(diǎn)和“連續(xù)性的矛盾問(wèn)題,接觸到了個(gè)別與全體、間斷性與連續(xù)性的對(duì)立統(tǒng)一問(wèn)題,

15、對(duì)促進(jìn)理性和經(jīng)驗(yàn)的辯證結(jié)合做出了一定的奉獻(xiàn)。三、牛頓、萊布尼茲創(chuàng)立微積分之比擬牛頓和萊布尼茲用各自不同的方法,創(chuàng)立了微積分學(xué)。如果說(shuō)牛頓接近最后的結(jié)論要比萊布尼茲早一些,那么萊布尼茲發(fā)表自己的結(jié)論要早于牛頓。雖然牛頓的微積分應(yīng)用遠(yuǎn)遠(yuǎn)超過(guò)萊布尼茲的工作,刺激并決定了幾乎整個(gè)十八世紀(jì)分析的方向,但是萊布尼茲成功地建立起更加方便的符號(hào)體系和計(jì)算方法。兩位微積分的奠基人,一位具有英國(guó)式的處事謹(jǐn)慎,治學(xué)嚴(yán)謹(jǐn)?shù)娘L(fēng)度,一位具有德國(guó)人的哲理思辨心態(tài),熱情大膽。由于陰陽(yáng)過(guò)失的時(shí)代背景, 過(guò)分追求嚴(yán)謹(jǐn)?shù)呐ｎD遲遲未將自己的發(fā)現(xiàn)發(fā)表,讓萊布尼茨搶了一個(gè)發(fā)表的頭籌。牛頓和萊布尼茲的哲學(xué)觀點(diǎn)的不同導(dǎo)致了他們創(chuàng)立微積分的方

16、法不同。牛頓堅(jiān)持唯物論的經(jīng)驗(yàn)論,特別重視實(shí)驗(yàn)和歸納推理。他在研究經(jīng)典力學(xué)規(guī)律和萬(wàn)有引力定律時(shí),遇到了一些無(wú)法解決的數(shù)學(xué)問(wèn)題,而這些數(shù)學(xué)問(wèn)題用歐幾里德幾何學(xué)和16 世紀(jì)的代數(shù)學(xué)是無(wú)法解決的,因此牛頓著手研究新的以求曲率、面積、曲線的長(zhǎng)度、重心、最大最小值等問(wèn)題的方法流數(shù)法?！芭ｎD的研究采用了最初比和最后比的方法。他認(rèn)為流數(shù)是初生量的最初比或消失量的最后比。初生量的最初比就是在初生的瞬間的比值,消失量的最后比就是量在消失的瞬間的比值。4 (p. 180) 這個(gè)解釋太模糊了,算不上精確的數(shù)學(xué)概念,只不過(guò)是一種直觀的描述。最初比和最后比的物理原型是初速度與末速度的數(shù)學(xué)抽象,在物體作位置移動(dòng)的過(guò)程中的每

17、一瞬間具有的速度是自明的,牛頓就是從這個(gè)客觀事實(shí)出發(fā)提出了最初比和最后比的直觀概念。這樣他就給出了極限的觀點(diǎn)。萊布尼茲的微積分創(chuàng)造始于研究“切線問(wèn)題和“求積問(wèn)題,他從微分三角形認(rèn)識(shí)到:求曲線的切線依賴于縱坐標(biāo)之差與橫坐標(biāo)之差的比值;求曲邊圖形的面積那么依賴于在橫坐標(biāo)的無(wú)限小區(qū)間上的縱坐標(biāo)之和或無(wú)限薄的矩形之和。萊布尼茲認(rèn)識(shí)到求和與求差運(yùn)算是可逆的。萊布尼茲用無(wú)窮小的思想給出了微積分的根本定理,并開(kāi)展成為高階微分。萊布尼茲的無(wú)窮小是分階的,這源于他哲學(xué)中的單子論思想。“萊布尼茲在單子論中指出:不同的單子其知覺(jué)的清晰程度是不一樣的,并從一種知覺(jué)向另一種知覺(jué)過(guò)渡和變化,開(kāi)展就是由單子構(gòu)成的事物,由低

18、級(jí)向高級(jí)的不同等級(jí)的序列。6 (p. 91) 可以說(shuō),萊布尼茲的無(wú)窮小的分階正是和它的客觀唯心論的哲學(xué)體系中那個(gè)不同層次的單子系統(tǒng)是相對(duì)應(yīng)的。萊布尼茲在微積分的研究過(guò)程中,連續(xù)性原那么成為其工作的基石,而連續(xù)性原那么是扎根于他哲學(xué)中無(wú)限的本質(zhì)的思想；牛頓和萊布尼茲創(chuàng)立微積分的相同點(diǎn)有:從不同的角度；牛頓和萊布尼茲創(chuàng)立微積分的不同點(diǎn)主要有:牛頓繼承；牛頓認(rèn)為微積分是純幾何的自然延伸,關(guān)心的是微積分；牛頓和萊布尼茲都是他們時(shí)代的科學(xué)巨人；參考文獻(xiàn):；1恩格斯.自然辯證法M.北京:人民出版社；2李文林.數(shù)學(xué)史概論M.北京:高等教育出；3杜瑞芝.數(shù)學(xué)史性原那么是扎根于他哲學(xué)中無(wú)限的本質(zhì)的思想。牛頓和萊

19、布尼茲創(chuàng)立微積分的相同點(diǎn)有:從不同的角度創(chuàng)立了一門(mén)新的數(shù)學(xué)學(xué)科,使微積分具有廣泛的用途并能應(yīng)用于一般函數(shù);用代數(shù)的方法從過(guò)去的幾何形式中解脫出來(lái);都研究了微分與反微分之間的互逆關(guān)系。牛頓和萊布尼茲創(chuàng)立微積分的不同點(diǎn)主要有:牛頓繼承了培根的經(jīng)驗(yàn)論,對(duì)歸納特別青睞。牛頓的微積清楚顯帶著從力學(xué)脫胎而來(lái)的物理模型的痕跡,以機(jī)械運(yùn)動(dòng)的數(shù)學(xué)模型出現(xiàn),其中的根本概念,如初生量、消失量、瞬、最初比和最后比等概念都來(lái)自機(jī)械運(yùn)動(dòng),是機(jī)械運(yùn)動(dòng)瞬間狀態(tài)的數(shù)學(xué)抽象。他建立微積分的目的是為了解決特殊問(wèn)題,強(qiáng)調(diào)的是能推廣的具體結(jié)果。而萊布尼茲強(qiáng)調(diào)能夠應(yīng)用于特殊問(wèn)題的一般方法和算法,以便統(tǒng)一處理各種問(wèn)題。萊布尼茲在符號(hào)的選擇

20、上花費(fèi)了大量的時(shí)間,創(chuàng)造了一套富有提示性的符號(hào)系統(tǒng)。他把sum(和) 的第一個(gè)字母S 拉長(zhǎng)表示積分,用dx 表示x 的微分,這套簡(jiǎn)明易懂又便于使用的符號(hào)一直沿用至今。牛頓認(rèn)為微積分是純幾何的自然延伸,關(guān)心的是微積分在物理學(xué)中的應(yīng)用。經(jīng)驗(yàn)、具體和謹(jǐn)慎是他的工作特點(diǎn),這種拘束的做法,使他沒(méi)有能盡情發(fā)揮。而萊布尼茲關(guān)心的是廣泛意義下的微積分,力求創(chuàng)造建立微積分的完善體系。他富于想象,喜歡推廣,大膽而且有思辯性,所以毫不猶豫地宣布了新學(xué)科的誕生。牛頓和萊布尼茲都是他們時(shí)代的科學(xué)巨人。 微積分之所以能成為獨(dú)立的學(xué)科并給整個(gè)自然科學(xué)帶來(lái)革命性的影響,主要是靠了牛頓與萊布尼茲的工作。從牛頓和萊布尼茲創(chuàng)立微積

21、分的過(guò)程中可以看出:當(dāng)巨人的哲學(xué)的沉思變成科學(xué)的結(jié)論時(shí),對(duì)科學(xué)開(kāi)展的影響是深遠(yuǎn)的。參考文獻(xiàn):1 恩格斯. 自然辯證法M . 北京:人民出版社,1971.2 李文林. 數(shù)學(xué)史概論M . 北京:高等教育出版社,2003.3 杜瑞芝. 數(shù)學(xué)史辭典M . 山東:山東教育出版社,2000.4 吳文俊. 世界著名科學(xué)家傳記M . 北京:科學(xué)出版社,1994.5 C H 愛(ài)德華. 微積分開(kāi)展史M . 北京:北京出版社,1989.6 M 克萊因. 古今數(shù)學(xué)思想M . 上海:上?？茖W(xué)技術(shù)出版社,1979.7 費(fèi)爾巴哈. 對(duì)萊布尼茲哲學(xué)的表達(dá)、分析和批判M . 北京:商務(wù)印書(shū)館,1985.Newton and L

22、eibniz created calculus resolutionAbstract: This paper mainly discusses the background of the times of Newton and Leibniz, and their philosophy of its founder is widely used in various fields of natural science basic mathematical tools - calculus.Key words: Newton; Leibniz; calculus; philosophical t

23、houghtToday, calculus has become the basic mathematical tools are widely used in various fields of natural sciences. Engels said: "in all theoretical achievements, not like the invention of the first half of the 17th century calculus as be seen as the highest victory for the human spirit, somew

24、here, we see the human spirit pure and only merit, it is in here. "1 (p. 244) This paper tries from Newton, Leibniz founded the historical background and philosophy" is seen as the highest victory of the human spirit "calculus its Expand profilingFirstly,Newtons background of the time

25、s and philosophy"Newton (Isaac Newton, born in 1642 - 1727) was born in 1642 in England. ? ?, in 1661, he got into the University of Cambridge, in1665, London was popular in plague, Newton returned to the countryside, all day he was thinking about a variety of issues, used his wisdom and severa

26、l years the knowledge, invented the number of flow cytometry (calculus), the analysis of the gravity and light. "2 (p. 155)On may 20, 1665, Newton's manuscript had the record of “the number of streams surgery. <The introduction of flow> , <movement to solve the problem >, other

27、papers in the number of streams (differential) and integration, and solution flow equation with integral table. In 1669, Newton circulated entitled "the use of an infinite number of equations analytics booklet in his friends, here, Newton was not only seeking a variable universal method for the

28、 instantaneous rate of change in another variable, but alsoproved that the area can be obtained by seeking the inverse process of the rate of the area is also used to represent the thus obtained. Newton proved this can be obtained by the inverse process of seeking the rate of change (more precisely,

29、 and the limit can be obtained by the anti-differential), the fact is that we are now talking about fundamental theorem of calculus. where, "Newton used the infinitesimal method, called" instantaneous "infinitely small increment of the variable, instantaneous infinitesimal, is not com

30、ponent or infinitesimal, Newton obtained abandon the" instantaneous "rate of change." 3 (p. 199)In 1671 Newton made his results on the study of calculus organized into flow method and the infinite series (1736), where, he believed that the variable was continuous motion generated vari

31、able called flow the rate of change of a variable was called the number of streams. Newton stated more clearly the basic problems of the calculus: the relationship between the two streams were known, found the relationship between the number of their flow, as well as its inverse problem. "The n

32、umber of streams law and infinited series" was a more complete calculus book. The second half of the book passed by 20 problems introduced a number of streams infinite series application of the 1676, Newton wrote "seeking curved edge-shaped area" (1704), where the thinking of Newton&#

33、39;s calculus significant changed, he gave up a micro or infinitesimal, while used the initial and The last ratio method. In 1687 Newton published its landmark scientific books "mathematical principles of natural philosophy, the number of flow cytometry (Calculus) was one of the three major fin

34、dings. As Einstein said: "Newton ? ? road you have found in your era is the one with the highest of thinking and creative skills of people who found the only way you created the concept even today still guiding our thinking in physics ". 4 (p. 192)Newton lived in an age Britain was changin

35、g times, when the British brake the civil war, the bourgeoisie and the aristocracy class compromised, made the bourgeois revolution in Britain not have thoroughness. The British bourgeois superstructure to do eternal argument for all the existence of the exploiting classes , therefore the absolute i

36、deological become the dominant ideology of the dominant, it also affected the naturalscientists absolute metaphysical way of thinking . Newton's ideas have also been a bourgeois revolution in Britain did not thoroughly Thus Newton often can not find the initial the cause from the nature or the t

37、hings of itself ,and by means of the external driving force.Before the age of 30, Newton discovered calculus, and established Classical Mechanics. However, he spended almost nothing on the study of the natural sciences. This was in capitalism and the formation period, the bourgeoisie had to theology

38、 attack to help liberate science from theology. But, When the bourgeois entrenched, the gradual intensification of the class struggle, the bourgeoisie gradually declined, they seized a wide variety of religious beliefs as slavery ideological weapon of the people. Newton influenced by its former life

39、 due to the ideological tendency of spontaneous materialism, he was a great achievement, the latter half was completely addicted to the study of theology.Newton inherited the tradition of Bacon's empiricism, special attention to the role of experimentation and inductive reasoning, he asserted th

40、e natural science can only explain the world starting from the empirical facts. This was for advocating talked against scholasticism, misuse the divine to distort the nature played a positive role. However, Newton was rigidly adhere to the empirical facts, one-sided emphasis on the importance of ind

41、uction. Emotional material, all stuck in the phenomenon of things, relying solely on the inductive method was to have no system of universal rational knowledge to. on the issue of analysis and synthesis, deductive and inductive metaphysics Newton caught in a contradiction. "5 (p. 123)Secondly,L

42、eibnizsbackground of the times and philosophyLeibniz (Gottfried Wilhelm Leibniz, 1646 - 1716) was born in Germany. ? ?, 1672 in Paris, where exposured to the Huygens some mathematical celebrities, to lead into the field of mathematics, the beginning of the calculus creativework 2 (p. 165)In 1684, Le

43、ibniz published the first official history of mathematics calculus literature, "a demand limit and tangent method. This literature of summarized results of the study of calculus since 1673, which defined the differential, extensively used the differentialsymbol dx, dy, and also gived the sum, c

44、ommossion,accumulated, and quotient the power of the rules of differentiation. Including the application of the differential method in the tangent line, great minima and inflection. Two years later, he published a a calculus thesis "esoteric geometry and not Variables and their infinite analysi

45、s ", which for the first time using the integral symbol " preliminary discusses the points (or quadrature) problem with differential quadrature tangent reciprocal problem. Well-known Newton - Leibniz formula BA f (x) dx = f (b) - f (a), gave us an outline of the basic shape of the calculus

46、 and the blueprint for the development.Newton's calculus was the departure from the point of view of kinematics, Leibniz from geometry viewed to consider the creation of calculus symbol was far better than Newton's symbol, and effectively promoted the development of the calculus of6 (p. 120) Newton discovered calculus (1665 - 1666) at least nine years earlier than Leibniz, Leibniz, however, published its calculus article three years earlier than Newton. According to the evidence be provided by the Leibniz himself that he formed in 1674,