抽象数学

For a long time, people mainly pay attention to the study of mathematics abstract thinking , while rarely care for mathematics visual thinking.

长期以来，人们对数学抽象思维的研究关注较多，而对于数学形象思维却问津较少。

Several combining with middle school mathematics teaching Abstract: combining the number is the number of more abstract corresponding relation and the geometrical graph, combine to solve the problem of abstract concepts to materialize and intuitive, intuitive, abstraction, and systematic problem to reduce the difficulty of the problem, and to help students thinking transformation and training students' ability.

数形结合与中学数学教学摘要：数形结合就是把较为抽象的数量关系和与其对应的几何图形相互结合起来解决问题，使抽象的概念直观化、具体化，使直观的问题系统化、抽象化，从而达到降低难题的难度、帮助学生思维转换、培养学生能力的作用。

The hydraulics are many more abstract concepts, such as water down on the physical process Flash animation can be used to form the wall with time changes, Piezometric head with time changes, pressurized pipe flow direction using flash animation shows, to reflect the vertical bisector and angle bisector of the rich multimedia features of the form can abstract mathematical concept into accommodation acceptable to the visual form.

在水力学中有许多较为抽象的概念，如水击的物理过程，可以用FLASH动画的形式将管壁随时间的变化过程，测压管水头随时间的变化过程，有压管中的水流方向用flash动画表现出来，以体现垂直平分线和角平分线的特点多媒体丰富的表现形式能使抽象的数学概念变为学生容易接受的直观形式。

The hydraulics are many more abstract concepts, such as water down on the physical process Flash animation can be used to form the wall with time changes, Piezometric head with the time change, pressurized pipe flow direction using flash animation shows, to demonstrate vertical bisector and angle bisector of the rich multimedia features of the forms make an abstract mathematical concept into accommodation acceptable to the visual form.

在水力学中有许多较为抽象的概念，如水击的物理过程，可以用FLASH动画的形式将管壁随时间的变化过程，测压管水头随时间的变化过程，有压管中的水流方向用flash动画表现出来，以体现垂直平分线和角平分线的特点多媒体丰富的表现形式能使抽象的数学概念变为学生容易接受的直观形式。

The higher mathematics curriculum is a college engineering course undergraduate course each specialized student's compulsory important basic theory class, through this curriculum study, causes the student to obtain: Circular function calculus study, the space analytic geometry and the vector algebra, the function of many variables calculus study, the infinite series, aspect and so on ordinary differential equation basic concepts, the elementary theory and the fundamental operation skill, and further obtain mathematics knowledge for the study successor curriculum to lay the essential mathematics foundation,During instruction knowledge, must train the student through each teaching link to have the abstract thinking ability, logic reasoning ability, spatial imagination ability gradually and studies independently ability, but also must pay attention specially trains the student to have the quite skilled operational capability and the synthesis utilization studies the knowledge to analyze the question and to solve the question ability.

高等数学课程是高等学校工科本科各专业学生的一门必修的重要基础理论课，通过本课程的学习，使学生获得：一元函数微积分学，空间解析几何与向量代数，多元函数微积分学，无穷级数，常微分方程等方面的基本概念、基本理论和基本运算技能，为学习后继课程和进一步获得数学知识奠定必要的数学基础，在传授知识的同时，要通过各个教学环节逐步培养学生具有抽象思维能力、逻辑推理能力、空间想象能力和自学能力，还要特别注意培养学生具有比较熟练的运算能力和综合运用所学知识去分析问题和解决问题的能力。主要是其中的一些专有名词查不到，比如一元函数等

The value of mathematics is lost.This article clarifies the nature and role of mathematical modeling thought,This thought will change abstract into image,change theory into application,and illustrates that this thought is necessary and feasible in higher algebra teaching.Melting modeling thought will be able to solve the...

数学建模思想就是将知识由抽象转化为形象，由理论转化为应用的思想，在高等代数教学中融入数学建模思想是必要的也是可行的，研究与实践表明，数学建模思想对培养人的创新思维及数学应用意识，提高教学质量以及学生的数学素质方面起着重要的作用。

Under these cir-cumstances,we were organ ized to compile"Infinitesimal Calculus and the Basis of Applied Math-ematics",which is a new mathematics teac...

作为高等职业教育公共基础课的数学教材，该书采用模块式、手册型，突出高职教育的应用性，便于自学，达到大学专科水平，注重对学生进行数学素质教育，特别重视培养学生的计算能力和抽象类比能力。并探索了将数学建模和计算机应用引入课堂教学。

This course mainly contents real number muster and function, limit of number sequence, limit of function, continuity, derived number and differential, differential mean value theorem and its application, completeness of real number, integral, series(including positive series and Fourier series), multiple- differential, double integral, integral with parameter, curve integral, camber integral and so on.

理解和掌握《数学分析》的概念、理论和方法，对于学生加深理解数学的基本思想和方法，培养抽象思维能力和逻辑思维能力，提高数学素养具有重要的意义。主要内容包括：实数集和函数，数列极限，函数极限，连续性，导数和微分，微分中值定理及其应用，实数完备性，积分、级数(包括幂级数、Fourier级数)、多元微分学、重积分、含参变量积分、曲线积分、曲面积分等。

The methods quantitatively analyze the mathematical abstraction and can help revealing the inner construction of mathematical theory with rich connotation by means of the theory of partial order set and graph theory, and so on.

该方法给出了数学抽象的定量分析，主要是应用了偏序集理论和图论等一些数学方法，它有助于揭示具有丰富内涵的数学理论的内在结构。

This thesis investigates the profile extraction and shape optimization on the result of topology optimization of planar compliant mechanisms. The main context includes the following work:(1) summarizing and analyzing the recent research status, some harvest and unsolved problems;(2) analyzing the conceptual design of planar path-generating compliant mechanisms and its mathematical model and tools;(3) Modifying the method of density contour as the method of profile extraction, and developing a method to optimize the density function in the profile extraction according to the requirement of the design of compliant mechanism;(4) developing a method to abstract the compliant mechanism into a form of links and joints by using the principle of connectivity on topology;(5) developing a method of shape optimization of planar path-generating compliant mechanisms, by representing the profile of the abstracted compliant mechanism as simple curves such as straight lines and arcs, establishing the models of the size optimization of the parameters of these curves, so that the compliant mechanism has a machinable shape;(6) At last, proving the feasibleness and effectiveness of the design method by making simulation design and validating it in FEA software.

主要工作包括：(1)分析了柔顺机构拓扑优化和形状优化的研究现状，分析了目前柔顺机构的研究重点、主要成果和尚未解决的问题；(2)分析了基于SIMP的柔顺机构概念设计方法及其相关工具和模型；(3)针对柔顺机构轮廓提取的特殊要求，提出了密度等值线法的改进方案，对密度函数插值点密度值进行优化，提出优化模型和选择优化算法；(4)根据轨迹输出平面全柔顺机构自身的形状特点，提出了轨迹输出平面全柔顺机构的抽象方法，即应用拓扑学上的连通性原理将柔顺机构抽象成杆件和结点形式，并对相应的数学原理进行了证明；(5)提出了平面全柔顺机构的形状还原和尺寸优化方法，对抽象的柔顺机构进行还原，将其轮廓还原成简单曲线的连接，从而建立尺寸优化模型，对机构进行尺寸优化设计，在得到可加工的机构轮廓的同时又能对关键部位进行特别处理；(6)进行了柔顺机构的数值仿真设计，并将所得设计结果导入商用有限元软件中进行仿真实验，证明了设计方法的可行性和有效性。

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。