反常積分與無(wú)窮級(jí)數(shù)收斂關(guān)系的討論畢業(yè)論文-展示頁(yè)
2025-07-06 23:08本頁(yè)面
【正文】 的求解探究另一類(lèi)問(wèn)題的解法,從而使讀者體會(huì)離散與連續(xù)的相互轉(zhuǎn)化思想,學(xué)會(huì)數(shù)學(xué)知識(shí)的遷移.關(guān)鍵詞：反常積分；無(wú)窮級(jí)數(shù)；對(duì)比研究；審斂法 Abstract Mathematical analysis is a subject mainly studying on variables, including the continuous and discrete ones. Series and integrals are two important concepts of it, there is a close relationship between them. They embodies the opposite and uniformity of basic contradiction of continuity and discreteness. So doing further research on the relationship between the two terms helps us to understand mathematical analysis principle, and to solve some related questions. Both seem to produce a conservationbased legacy with source. They are peace operations, is merely to two different variables summation, at the same time is a limit process, so continuous questions of integral theory (generalized integrals, with respect to the integral, etc.) and discretization questions of series (several series, function of series) have many properties, theorem are mutual correspond, both in research on problems with similar reasoning methods. By paring the concepts, convergence, nature and discriminant method of both aspects, this article lists many paralleled conclusions and some differences, as well as the translation between them. And solve some problems of one kind by applying the solutions of the other kind, thus helping the readers to realize the transformation between discrete and continuous thoughts, and be able to learn mathematics knowledge migration.Keywords Improper integral。 Infinite series。 The Inspection Technique 目錄第1章 緒論 1 選題背景及意義 1 問(wèn)題的提出 1 相關(guān)文獻(xiàn)綜述 2 論文的主要結(jié)構(gòu) 3第2章 反常積分的收斂方法 4 4 5 7第3章 無(wú)窮級(jí)數(shù)的收斂方法 8 無(wú)窮級(jí)數(shù)的概念 8 8 12第4章 無(wú)窮級(jí)數(shù)與無(wú)窮積分的關(guān)系探討 15 15 16 17 19結(jié)束語(yǔ) 20致謝 21參考文獻(xiàn) 22第1章 緒論 選題背景及意義級(jí)數(shù)和反常積分是微積分學(xué)中的重要內(nèi)容,微積分又是以極限為工具來(lái)研究數(shù)學(xué)內(nèi)容的 .數(shù)學(xué)分析也叫微積分學(xué)它是在17世紀(jì)中葉由牛頓和萊布尼茨創(chuàng)立,由麥克勞林、泰勒、達(dá)郎貝爾、拉格郎日等數(shù)名數(shù)學(xué)家,歷經(jīng)200多年的發(fā)展和完善直到19世紀(jì)末才形成現(xiàn)今我們說(shuō)的數(shù)學(xué)分析主要內(nèi)容 .對(duì)于級(jí)數(shù)主要包括數(shù)項(xiàng)級(jí)數(shù)、交錯(cuò)級(jí)數(shù)、函數(shù)項(xiàng)級(jí)數(shù)、冪級(jí)數(shù)以及傅里葉級(jí)數(shù)等主要內(nèi)容；反常積分也稱(chēng)廣義積分主要包括無(wú)窮積分和瑕積分兩方面內(nèi)容；反常積分是學(xué)習(xí)了定積分后又一新的內(nèi)容,是對(duì)定積分的進(jìn)一步推廣,反常積分打破了定積分的區(qū)間有窮性和被積函數(shù)的有界性限制,無(wú)窮積分主要研究的是無(wú)窮區(qū)間上的“積分”問(wèn)題,瑕積分主要研究的是無(wú)界函數(shù)的積分問(wèn)題 ,它們的共同點(diǎn)都是以極限為工具轉(zhuǎn)化為我們熟悉定積分問(wèn)題進(jìn)行研究的 . 問(wèn)題的提出 本論文想通過(guò)對(duì)反常積分和數(shù)項(xiàng)級(jí)數(shù)以及它們的含參量形式這兩對(duì)概念的定義、性質(zhì)、收斂判別法等方面加以比較,列出相平行
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