数学毕业论文曲线拟合在数学建模中的应用

1、曲线拟合在数学建模中的应用目录 摘 要1Abstract2 前言31 数学建模简介41.1数学建模的概念41.2数学建模的 1 般方法和步骤41.3数学建模的重要意义42 MATLAB简介52.1组成52.2MATLAB语言 63 曲线拟合83.1曲线拟合理论83.2曲线拟合的最小 2 乘法83.3线性最小 2 乘法93.4直线拟合 103.5多项式拟合103.6用 MATLAB作线形最小2 乘拟合 114 MATLAB与曲线拟合在水塔流量估计模型中的应用144.1问题的提出144.2问题分析144.3模型假设144.4流量估计的解题思路154.5算法设计与编程154.6分析与改进235 结束

2、语 24 参考文献25 致谢 26摘 要数学建模方法是处理科学理论的1 种经典方法，也是解决各类实际问题的常用方法。通过抽象、简化、假设、引进变量等处理过程后，将实际问题用数学方式表达，建立起数学模型，然后运用先进的数学方法及计算机技术进行求解。曲线拟合通俗地讲就是用 1 条( 或 1 族 ) 适当的曲线去模拟 1 组( 或多组 ) 实验数据，从而得到较好地符合实验事实的数学关系式。 MATLAB是 1 种广泛应用于工程计算及数值分析领域的新型高级语言。本文探讨了 MATLAB 这 1 强而有力的工具在实验数据分析和处理中的应用。将测量中得到的水塔流量的相关数据运用最小 2 乘法，通过编写程序

3、实现向计算机输入实验测量数据，由 MATLAB计算求出其函数表达式，明确表示出各物理量之间的关系。同时在屏幕上作出函数表达式的曲线，实现了数据分析和处理的快捷、准确和直观。计算结果与实际记录基本吻合。关键词：数学建模；曲线拟合；水塔流量AbstractMathematics modelling is a classical method to theprocess scientific theory . Also, its a common methodto solve all kinds of actual problems. Through theprocessing of abstrac

4、t, simplification, supposition andintroduction variable, we can express the actual problemwith mathematics, establish the mathematical model, andadopt the advanced mathematics method and computertechnology to carry on the solution . Generally speaking,the curve fitting is to use a suitable curve imi

5、tating, agroup with (or multi-groups) the empirical datum, andthen abtain mathematics relationship in line with thefact well. MATLAB is a new advanced language applying inthe field of engineering calculation and the numericalanalysis . This article will discuss MATLAB thispowerful tool applying in t

6、he empirical datum analysisand processing. Utilize the relevant data about the flowof the water tower acquired in survey to realize theinput of survey data for erperient into thecomputer ,first by way of the lowese square metheod andlater through programming; then, the function expressionwill be wor

7、ked out through MATLAB computation ,and therelationship between various physical volume can beshowed clearly. Meanwhile the curve of functionexpression on the screen makes it quick, accurate anddirect for figures analying and processing. The computedresult corresponds to the real record basically.Ke

8、y wordsmathematics modeling; curve fitting ; water tank current：capacity目录 摘 要 1Abstract2 前言31 数学建模简介41.1数学建模的概念41.2数学建模的 1 般方法和步骤41.3数学建模的重要意义42 MATLAB简介52.1组成52.2MATLAB语言 63曲线拟合83.1曲线拟合理论83.2曲线拟合的最小 2 乘法83.3线性最小 2 乘法93.4直线拟合103.5多项式拟合103.6用 MATLAB作线形最小2 乘拟合114 MATLAB与曲线拟合在水塔流量估计模型中的应用144.1问题的提出144

9、.2问题分析144.3模型假设144.4流量估计的解题思路154.5算法设计与编程154.6分析与改进235 结束语24 参考文献 25 致谢 26摘 要数学建模方法是处理科学理论的1 种经典方法，也是解决各类实际问题的常用方法。通过抽象、简化、假设、引进变量等处理过程后，将实际问题用数学方式表达，建立起数学模型，然后运用先进的数学方法及计算机技术进行求解。曲线拟合通俗地讲就是用 1 条( 或 1 族) 适当的曲线去模拟 1 组( 或多组 ) 实验数据，从而得到较好地符合实验事实的数学关系式。 MATLAB是 1 种广泛应用于工程计算及数值分析领域的新型高级语言。本文探讨了MATLAB这 1

10、强而有力的工具在实验数据分析和处理中的应用。将测量中得到的水塔流量的相关数据运用最小2 乘法，通过编写程序实现向计算机输入实验测量数据，由MATLAB计算求出其函数表达式，明确表示出各物理量之间的关系。同时在屏幕上作出函数表达式的曲线，实现了数据分析和处理的快捷、准确和直观。计算结果与实际记录基本吻合。关键词：数学建模；曲线拟合；水塔流量AbstractMathematics modelling is a classical method to theprocess scientific theory . Also, its a common methodto solve all kinds

11、of actual problems. Through theprocessing of abstract, simplification, supposition and introduction variable, we can express the actual problem with mathematics, establish the mathematical model, and adopt the advanced mathematics method and computer technology to carry on the solution . Generally s

12、peaking, the curve fitting is to use a suitable curve imitating, a group with (or multi-groups) the empirical datum, and then abtain mathematics relationship in line with thefact well. MATLAB is a new advanced language applying in the field of engineering calculation and the numericalanalysis . This

13、 article will discuss MATLABthispowerful tool applying in the empirical datum analysisand processing. Utilize the relevant data about the flow of the water tower acquired in survey to realize the input of survey data for erperient into thecomputer ,first by way of the lowese square metheod andlater through programming; then, the function expressionwill be worked out through MATLAB computation ,and therelationship between various physical volume can be showed clearly. Meanwhile the curve of function expression on th