函數(shù)方程的一些解法畢業(yè)論文

目    錄
摘    要 ..........................................................II
Abstract.......................................................... III
前    言.......................................................... 1
第一章  單變量遞推形式函數(shù)方程的一些解法................ ..........2
1.1  換元法.................................. .....................2
1.2  構(gòu)造方程組法.................................. ..............3
1.3  待定系數(shù)法....................................................3
1.4  極限法................................................... ....4
1.5  定義法................................................... ....5
第二章 雙變量遞推形式函數(shù)方程的一些解法................ ..........6
2.1 遞歸法.................................. ................ .....6
2.2 轉(zhuǎn)化法.................................. .............. ......7
2.3 微積分法.................................. .............. .....8
2.4 賦值法.........................................................9
第三章 微分積分形式函數(shù)方程的一些解法................ .......... ..10
3.1 常微分法.................................. .............. ......11
3.2 積分法.................................. .............. ........13
第四章 隱函數(shù)方程的一些解法................ .......... ......... ..14
4.1 不動(dòng)點(diǎn)法.................................. ............. .......14
結(jié)    論................................ ......... ..... .. .... .. ..17
參考文獻(xiàn)................ ................ ...........................18
致    謝................. ............... ......... .................19 

摘    要
   
本文討論函數(shù)方程的一些解法。
在第一章，我們介紹單變量遞推形式函數(shù)方程的一些解法，以構(gòu)造方程組法、待定系數(shù)法、極限法、換元法這四種方法為主要研究?jī)?nèi)容。
在第二章，我們介紹雙變量遞推形式函數(shù)方程的一些解法，如：柯西遞歸法、轉(zhuǎn)化法、微積分法、賦值法。
在第三章，我們介紹微分積分形式函數(shù)方程的一些解法,主要有分離變量法、湊微分法、拉普拉斯變換法、常數(shù)變易法等。
在第四章，我們將探討一種特殊隱式函數(shù)方程。

關(guān)鍵詞：函數(shù)方程，微分方程，單變量，雙變量、解

 
Abstract
      In the paper, we study some methods to solve function equations.
In the first chapter，we introduce some methods to solve function equations with some recursive form with one variable. It contains four main research methods: structural equations method, undetermined coefficients method, limit law methods, element method.
In the second chapter，we introduce some methods to solve function equations with some recursive form with two variable. It contains Cauchy recursive method, transformation method, calculus method, assignment method.
In the third chapter，we introduce some methods to solve function equations with differential or integral forms. It contains variables separation method, differential method, Laplace transform method, variation of constants method.
 In the fourth chapter, we will explore a special kind of implicit function equations

Key words: functional equation, differential equation, single variable, bivariable, solutions