内蒙古科技大学
李沐航本 科 毕 业 论 文
论文题目： 随机微分方程在物理学中的应用
院 系： 物理科学与技术学院
专 业： 应用物理
姓 名： vvv
学 号： ********** 关于孝道的故事
指导教师： xxx
二零 一二 年 三 月
摘要
牛顿和莱布尼兹创建了微积分学，为了描述机械动力学、天文学等领域的物理现象，建立了确定性的微分方程。确定性的微分方程在实际问题中有大量的应用。然而在研究实际物理现象的数学模型时，描述一个具体物理现象所用的一组数学方程不会是完全精确的。实际问题中不确定性因素大量存在且往往是问题的关键所在，不可忽视。由于二十世纪中叶大量的含有不确定性的实际问题的出现，以及对模型精确性要求和实际问题复杂性认识的不断提高，不确定性因素越来越多的被考虑到模型的建立中，这就在微分方程的基础上引入了随机因素，促使了随机积分的构建与发展，并在此基础上建立了随机微分方程的相关理论和方法。
随着科技的发展，随机微分方程越来越广泛地应用于模型的建立和分析中。本文针对物理学中存在随机性的特征，提取其中的数学本质，利用数学方法和策略，建立相应的随机微分方程，分析其中数学特征和数学机理，推导相关的公式和性质，通过分析来更好的理解物理学中的随机性问题。
护理
关键词：随机微分方程；布朗运动；matlab模拟；
Abstract.
Newton and Leibniz created calculus, in order to describe the mechanical dynamics, astronomy and other fields of physics, the establishment of a deterministic differential equation. Deterministic differential equations large number of practical problems in application. However, the actual physical phenomena in the study mathematical model to describe the physical phenomenon of a specific t of mathematical equations ud to not be completely accurate. Practical problems of uncertainties abound and often the crux of the problem can not be ignored. Since the mid-twentieth century, a lot of uncertainty with the actual problems, and the accuracy of the model and actual problems requires understanding the complexity of continuous improvement, more and more uncertainty to the model to be considered in This is the basis of the differential equations introduced random factor contributing to the construction and development of stochastic integral, and on this bad on the theory of stochastic differential equations and methods.
With the development of technology, more and more widely ud in stochastic differential
equation model and analysis. In this paper, the cha- racteristics of randomness exist in physics, mathematics extracted the es- nce, the u of mathematical methods and strategies, the大扫帚 政治必修一establishment of the corresponding stochastic differential equations, mathematical如何写对联 char- 什么是茶道 acteristics and mathematical analysis in which the mechanism and nature of the formula is derived through the analysis to better Understanding of stochastic problems in physics.
Key words:梅里雪山 stochastic differential equations; Brownian motion; matlab simulation;
