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关键词： 中高衔接   高等数学   导数   导数的应用   教学探讨  

摘要： 导数是高等数学的一个重点内容,是中职学校中高衔接班级高等数学教材的一个亮点。画函数的图像;求函数的值域;求函数的解析式;求解函数的斜率;求解函数极限;解决不等式的证明问题;进行数列求和及最大或最小项的求解;利用导数解决实际问题等等。笔者通过一些实例,介绍导数在实际教学中的应用,让学生认识导数这一知识点。本文将从我们中等职业学校学生的学情现状、导数概念产生的背景及导数的的实际应用等方面进行探讨。

关键词： 梁振动偏微分方程   微分–代数方程   L-稳定方法   非线性   稳定性  

摘要： 基于高阶非线性梁振动偏微分方程的一般形式,构造了数值求解的L-稳定格式。首先,选取三角插值基函数,基于插值定理进行空间离散,将带有初边值条件的偏微分方程求解问题转化为微分–代数方程求解。然后在时间区间上构造L-稳定求解格式进行求解。以无轴向运动简支梁在外部激励下的强迫振动方程为例进行数值仿真,对梁的位移轨迹、边界条件及系统能量进行探究,并与龙格–库塔法、微分求积法进行对比,结果表明,L-稳定方法可以在较大步长下满足边界,位移轨迹与模型方程一致,在计算精度和稳定性上都有较好的体现。

关键词： Age-space-structured PDF   Reaction-diffusion system with nonlocal term   Continuous difference equation   Traveling wave solution   SIR epidemic model  

摘要： We consider a general class of diffusive Kermack-McKendrick SIR epidemic models with an age-structured protection phase with limited duration, for example due to vaccination or drugs with temporary immunity. A saturated incidence rate is also considered which is more realistic than the bilinear rate. The characteristics method reduces the model to a coupled system of a reaction-diffusion equation and a continuous difference equation with a time-delay and a nonlocal spatial term caused by individuals moving during their protection phase. We study the existence and non-existence of non-trivial traveling wave solutions. We get almost complete information on the threshold and the minimal wave speed that describes the transition between the existence and non-existence of non-trivial traveling waves that indicate whether the epidemic can spread or not. We discuss how model parameters, such as protection rates, affect the minimal wave speed. The difficulty of our model is to combine a reaction-diffusion system with a continuous difference equation. We deal with our problem mainly by using Schauder's fixed point theorem. More precisely, we reduce the problem of the existence of non-trivial traveling wave solutions to the existence of an admissible pair of upper and lower solutions. (c) 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： 三角函数   有理式   不定积分  

摘要： 三角函数在微积分得到广泛应用,而积分学又是微积分的重要组成部分,不定积分则是积分学的核心内容.由于三角函数的性质特殊、公式灵活多变,就意味着三角函数有理式的积分的计算也非常灵活多变.在教学中通过对三角函数有理式的形式进行分析,探讨三角函数有理式的不定积分的解答方法,以掌握求不定积分中的各种方法之间的相互关系、拓展学生的解题思路并提高学生的计算能力、推理能力和观察能力,进而发展学生的创新思维能力、发散思维和综合能力.

关键词： 常微分方程   课堂教学   教学评价  

摘要： 根据民族实验班学生数学学习的现状，探讨常微分方程课程课堂、课下教学改革，提出一些具体的实践措施，取得了一定成效。

关键词： Atomic force microscopy   Holographic microscopy   Image processing   Phase contrast   Phase contrast imaging   Scanning electron microscopy  

摘要： In cardiovascular disorders, the study of thrombocytes, commonly known as platelets, is highly important since they are involved in blood clotting, essential in hemostasis, and they can in pathological situations affect the blood circulation. In this paper, single deposited platelets are measured using interferometric digital holographic microscopy. We have shown that the average optical height of platelets is significantly lower in healthy volunteers than in dialyzed patients, meaning a better spreading. It demonstrates the great interest for assessing this parameter in any patients, and therefore the high potential of analyzing single spread platelets using digital holographic microscopy in fundamental research as well as a diagnostic tool in routine laboratories, for usual blood tests. (c) 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

关键词： 高中数学函数   高中数学导数   逻辑推理   核心素养  

摘要： 高中数学函数与导数部分的教学工作中,对学生的逻辑推理能力要求较高,教师往往要兼顾两者,导致学生对函数与导数产生抽象、复杂的印象,在解题中导致思维出现矛盾现象,因此本文对函数与导数部分教学中的逻辑推理素养培养教学实践进行探究,以资参考.

关键词： 电磁感应   GeoGebra   微分方程   导体棒  

摘要： 在电磁感应的教学中，“滑轨与导体棒模型”作为高考的重点和难点具有非常多的变式。由于这类题型综合性强，学生难以理解问题的本质，故产生了许多认知障碍。本文基于GeoGebra软件，深入分析了“滑轨与导体棒模型”中负载为电阻和电容时，导体棒的运动情况，并通过微分方程对导体棒的运动规律做出科学解释。

关键词： 函数   导数   单调区间   取值范围  

摘要： 不等式恒成立条件下的参数取值范围问题是导数应用中的一类具有综合性与创新性的复杂应用,破解的关键是通过恒成立不等式的等价变换,合理构造函数,利用导数求导,综合考查学生的逻辑推理能力、数学运算能力等。

关键词： reconfigurable multiport photonic processor   N-differentiator   integrator   micro-ring resonator   thermo-optic phase shifters   three-dimensional finite-difference-time-domain  

摘要： At present, a high-order, reconfigurable photonic signal processor is very difficult to implement. A simple, reconfigurable photonic N-differentiator and integrator based on a unit of the dual-ring coupled Mach-Zehnder interferometer (DRMZI) is proposed first. The reconfigurability is achieved only by controlling the thermo-optic phase shifter (TO-PS) on the two improved micro-ring resonators. The device presents a wide fine-tunable differentiation order range from 0.2 <= N <= 1.7 reconfigured as a 2 x 2 differentiator after being optimized the TO-PS and the tunable couplers (TC). If it is reconfigured as an integrator, a first-order photonic temporal integrator with 16.1 GHz 3-dB bandwidth and integration time window 38.4 ps is achieved in our design. The 4 x 4 port DRMZI differential unit can be cascaded into k-stage to realize 0.2 x k <= N <= 1.7 x k order differential function, theoretically approaching any large order. At the same time, the differential signals can be successfully routed to different output ports by reconfiguring the optical path in the structure. The simulation results have shown that a two-stage 4 x 4 photonic temporal differentiator can perform more than two order differential operations, e.g., N = 2.4. Our research can provide a reference for chip-level large-scale integrated photonic processors. (C) 2022 Society of Photo-Optical Instrumentation Engineers (SPIE)