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大学数学中的数形结合思想
Several of the middle school Mathematics
form combining ideas
姓 名： 张晓锐 学 号： 学 院： 专 业：指导老师：完成时间：
51505111012
蚌埠学院
数学与应用数学
冯海亮
2017年2月23日
大学数学中的数形结合思想
【摘要】数形结合的思想，是通过数形间的对应与互助来研究并解决问题的思想，是最基本的数学思想之一。它可以使某些抽象的数学问题直观化、生动化，能够变抽象思维为形象思维，有助于把握数学问题的本质。正如我国著名数学家华罗庚对数形结合思想的精辟论述:“数以形而直观，形以数而入微”。我将从以下几个方面来探讨数形结合思想在大学数学中的应用：（1）在二重积分上的应用（2）在三重积分上的应用。通过分析、比较和归纳充分展现数形结合思想在解题中的特点和优越性，从而在实际教学中要将数形结合思想融汇到课堂中，培养学生加强数形结合思想的意识．
【关键词】大学数学 数形结合 应用 思想方法
Several of the university school Mathematics form
combining ideas
【Abstract】 In the uiversity school mathematics has lots of mathematical methods,
including several form combining ideas middle school mathematics is one of the most important methods, it will algebra and geometry, and the combination of using several shape transformation between, be helpful for analysis problem of the relation between the quantity, rich imagination, change numerous hard things simple, easy, on the one hand, graphic nature of many of the abstract will math concepts and visual and quantitative relationship between simplified, give a person with intuitive enlightenment. On the other hand, will graphics problem into the algebra problem, in order to obtain the accurate conclusions. Improve the analysis and problem solving ability so as to achieve simple problem solving method, the final convenient our problem solving. I will from the following several aspects to discuss several form combining ideas university school mathematics in the application: (1) the application of double integral; (2) the application of three integral(, domain in its application. Through the analysis, comparison and induction show several form combining ideas of problem in the characteristic and advantages, which in actual teaching will form together with several ideas to the classroom, training students' strengthen the consciousness of combining ideas number form.
【Key words】 school mathematics Several form combined with An
application example Thought method
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