常微分方程在数学建模中的应用

通过若干实例,运用高等数学中的微分方程方法建立数学模型,提高学生学习高等数学的兴趣并逐步了解数学建模的方法和思想;提高课堂讲课效果、实践素质教育改革.     

The Effects of a STEM Intervention on Elementary Students' Science Knowledge and Skills

The purpose of the study was to assess elementary students' science process skills, content knowledge, and concept knowledge after one year of participation in an elementary Science, Technology, Engineering, and Mathematics (STEM) program. This study documented the effects of the combination of intensive professional development and the use of inquiry‐based science instruction in the elementary classroom, including the benefits of using rigorous science curriculum with general education students. The results of the study revealed a statistically significant gain in science process skills, science concepts, and science‐content knowledge by general education students in the experimental group when compared with students in the comparison group. Moreover, teacher participation in the STEM program had a statistically significant impact on students' variability in posttest scores. These interim student performance data support the implementation of rigorous differentiated science curriculum focused on improving science concept, content knowledge, and process skills.     

在常微分方程教学中融入数学建模思想的探索与实践

结合常微分方程理论性强和应用性强的特点,探索如何在教材、教学方法等方面融入数学建模思想的方法.     

Differential Equations in Engineering Courses

This paper formed part of a research project carried out by the author into the mathematical education of engineers.¹ In this part of the work an attempt was made to assess the relative importance of various aspects of ordinary differential equations in the teaching of engineering students and to find out which types of equations were used in the various engineering disciplines. A questionnaire was circulated and the replies were collated to give the results.     

Differential Equations in Banach Algebras

Doklady Mathematics - In a complex Banach algebra that is not assumed to be commutative, nth-order linear differential equations with constant coefficients are considered. The corresponding...     

变量代换法在解微分方程中的应用

归纳总结利用变量代换求解不同类型常微分方程的方法与技巧,并借助两个实例的多种解法加以说明.     

Averaging of Backward Stochastic Differential Equations and Homogenization of Partial Differential Equations with Periodic Coefficients

Abstract

We study the limit of the solutions of systems of semi-linear partial differential equations (PDEs) of second order of parabolic type, with rapidly oscillating periodic coefficients, a singular drift, and singular coefficients of the zero and second order terms. Our basic tool is the approach given by Pardoux [14 Pardoux , E. 1999 . Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: a probabilistic approach . J. Funct. Anal. 167 : 498 – 520 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]]. In particular, we use the weak convergence of an associated backward stochastic differential equation (BSDE).     

关于知识增长和知识创新的数学模型

本文研究知识增长的一般规律 ,导出了一个描述知识增长规律的拟线性微分方程 x=(α+β-γ) x,为知识增长与知识创新的研究提供了数学模型 .由此模型 ,我们得到了几个有意义的结论 .     

More on Ordinary Differential Equations Which Yield Periodic Solutions of Delay Differential Equations

We construct a Poincaré operator for the system where λ is a real parameter, x ³, x = (x₁, x₂, x₃), [formula], and ƒ is an odd C² function such that ƒ′(0) = 1, xƒ(x) > 0, for x ≠ 0. We also consider the case where ƒ is C¹. We will express F in linearized form, that is, F(x) = Ax + G(x), where A is the linearized part of F around zero and G(x) = o(|x|) near zero. Fixed points of the Poincaré operator correspond to periodic solutions of the functional differential equation

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where T is the period of x.     

Oscillation and Nonoscillation in Delay or Advanced Differential Equations and in Integrodifferential Equations

Some new oscillation and nonoscillation criteria are given for linear delay or advanced differential equations with variable coefficients and not (necessarily) constant delays or advanced arguments. Moreover, some new results on the existence and the nonexistence of positive solutions for linear integrodifferential equations are obtained.     

Solving Equations and the Inverse of Mathematical Operations

Many of the simpler equation-solving problems in science and mathematics can be approached in a nontraditional way that de-emphasizes skills with algebra and calculus. This alternative procedure emphasizes an examination of the steps or operations necessary to perform a calculation, followed by the inversion of those steps. Specifically, each step is replaced by its inverse, and the steps are performed in reverse order. The approach is especially attractive to students with limited mathematical skills.     

数学的默会知识及其教学意义

讨论了数学默会知识的涵义以及主要特点,论述了数学默会知识对数学学习和数学研究的影响及其对数学教学的意义.     

Jounral of Partial Differential Equations

Aims and Scope：
The Journal of Partial Differential Equations （JPDE） publishes high quality research papers and short communications in theory, applications and numerical analysis of partial differential equations. Papers addressing new theoretical techniques, novel ideas, and new analysis tools are suitable topics for the journal.     

Journal of Partial Differential Equations

The Journal of Partial Differential Equations (JPDE) publishes research papers and short communications of high scientific quality in theory and applications including numerical analysis of partial differential equations. The main interest of the Journal is to encourage the research of partial differential equations, and to promote national and international exchange between partial differential equations, engineering, physics and different fields of mathematics.     

时滞微分方程的不共轭性

本文推广了共轭点和不共轭微分方程的概念，证明了时滞微分方程的不共轭区间不可能是一个单点集．此外，还证明了时滞微分方程的不共轭性与边值问题的可解性之间的联系．     

Jounral of Partial Differential Equations

Aims and Scope： The Journal of Partial Differential Equations （JPDE） publishes high quality research papers and short communications in theory, applications and numerical analysis of partial differential equations. Papers addressing new theoretical techniques, novel ideas, and new analysis tools are suitable topics for the journal.