函数方程的一些解法毕业论文.doc

函数方程的一些解法毕业论文

目    录
摘    要 ..........................................................II
Abstract.......................................................... III
前    言.......................................................... 1
第一章  单变量递推形式函数方程的一些解法................ ..........2
1.1  换元法.................................. .....................2
1.2  构造方程组法.................................. ..............3
1.3  待定系数法....................................................3
1.4  极限法................................................... ....4
1.5  定义法................................................... ....5
第二章 双变量递推形式函数方程的一些解法................ ..........6
2.1 递归法.................................. ................ .....6
2.2 转化法.................................. .............. ......7
2.3 微积分法.................................. .............. .....8
2.4 赋值法.........................................................9
第三章 微分积分形式函数方程的一些解法................ .......... ..10
3.1 常微分法.................................. .............. ......11
3.2 积分法.................................. .............. ........13
第四章 隐函数方程的一些解法................ .......... ......... ..14
4.1 不动点法.................................. ............. .......14
结    论................................ ......... ..... .. .... .. ..17
参考文献................ ................ ...........................18
致    谢................. ............... ......... .................19 

摘    要
   
本文讨论函数方程的一些解法。
在第一章，我们介绍单变量递推形式函数方程的一些解法，以构造方程组法、待定系数法、极限法、换元法这四种方法为主要研究内容。
在第二章，我们介绍双变量递推形式函数方程的一些解法，如：柯西递归法、转化法、微积分法、赋值法。
在第三章，我们介绍微分积分形式函数方程的一些解法,主要有分离变量法、凑微分法、拉普拉斯变换法、常数变易法等。
在第四章，我们将探讨一种特殊隐式函数方程。

关键词：函数方程，微分方程，单变量，双变量、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