类比思想在数学中的应用(英文论文)Analogythoughtinmathematicsapplication.doc

AnalogythoughtinmathematicsapplicationAbstractThrough to above problem solving method relating in detail, causes ourcerebrum sober understanding to the science thought method in theproblem solving process importance, these methods can cause the knowledge systematization which we studies, orderliness, then achievedunderstands by analogy boundary which and achieves mastery through acomprehensive study of a subject, in the review summary process, these methods appears in particularly importantly. Above stated only is elaborated the thought method from two different aspects in the problem solving application, but we discussed mathematics thought method the final goal enhance studentsmathematics accomplishment, so long as we in usual problem solving process bold practice, excavated in the teaching material and the exercise mathematics thought method, had the goal, has the plan these page, utilizes in the usual teaching and the problem solving training, our problem solving ability surely could strengthen Bacon once said that, the philosophy causes the person profoundly,reads the poem to cause the person intelligently, mathematics causesthe person fine, actually, mathematics not only causes the personfine, mathematics also can cause the person profoundly, causes theperson to be intelligent, each people all certainly want specially toread the philosophy by no means, also the non- each people all want tocompose a poem However, each people all must the reading study,practice mathematics, make mathematics, want long-term systematicallyto read and to practice, because mathematics truly not only practical,because it can cause us fine, more profound, is more intelligent Thusthe study mathematics process is the person has the creative thoughtessential processIt is well known, the mathematics education primary mission should beraises students creative mathematics ability and the solution actualproblem ability, thus causes the student to have the creativescientific ability, but creative ability manifesting is the creativethought development and the application, fosters method and skill Mathematics knowledge and mathematics method are in the entire humanknowledge structure two important constituent. But the knowledgecertainly cannot directly transform as the ability, this kind oftransformation must as intermediary be able to realize take thethought Thus mathematics knowledge (method) is mathematics thinkingactivity concrete application result, therefore said the entiremathematics teaching process is mathematics thinking activity processApplies the thought in the teaching and the exercise training,inevitably can raise students thought creativity But at present we to the teaching material and theexercise excavation Teaches the knowledge primarily, goes by thebook, does the excessive assignments tactic in the exercise training,overemphasizes the logical thinking, specially deducts the logic, butthese to develop the students latent creative ability to be verydisadvantageous, we must break through in the traditional mathematicsteaching mathematics thought purely to understand for the logicalthinking old idea, the induction, analogy, disperses, thought and soon reversion took one kind of union mathematics the contentcharacteristic carries on the teaching and the problem solvingtraining This article on take the higher mathematics in relatedcontent as regularly specifically said how these four kind of thoughtsmethod utilization and does raise students thought quality一、Analogy thought in mathematics application Analogy is one kind of creative thought form The famous philosopherconde pointed out that, When the reason lacks the reliable proof thementality, analogy this method often can direct us to go forward. Analogy is according to two or many objects interior attribute, therelational certain aspects is similar, but promotes them in otheraspect also possible similar inference methods Analogy has providedthe broader free creation big world for peoples thought process,causes it to become the scientific research Central Africa commoncreative thought form, thus is valued very many famous mathematiciansand the favour, if the renowned astronomer, the mathematician opensPuller to say: I treasure analogy to win to any other thing, it isteacher which I most may trust, it can promulgate the naturalmystery. Famous mathematician educationalist train of wave Asia saidthat, Analogy is great leads the way the person, the solutionthree-dimensional geometry question often depends on in the plane geometry the analogy question. Therefore, in study higher mathematics time, should take the analogy method For example, when study space analytic geometry related question,should with already has studied plane analytic geometry related question analogy For example: In the plane analytic geometry firstpower regulation is a straight line, in the space analytic geometry first power regulation is the planeIn plane analytic geometry the straight line is, In the space analytic geometry the plane is In the plane analytic geometry the round equation is, In the space analytic geometry the ball equation is and so on Specially, everybody in study function of many variables time sharing, certainly must already has studied with own a Yuan fluxionary calculus related content carry on analogy Also like, everybody after studied the definite integral, the double integral, the triple integral, the curvilinear integral, the surface integral, had to carry on these kind of integrals analogy, including theirs definition, nature, computational method, physics significance and so on First, everybody must discover that, these kind of productsall are press the division, the summation, take the limit several kind of integrals all may unify record are, is the primary function, If, is precisely time, then expression definite integral. If is precisely time the plane region ， then expresses thedouble integral If, is precisely time the space curve, then expression curve linear integral if, is precisely time a curved surface, then expression surface integralAlso like, if definite integral explanation for density for the tangential path pole quality, with the analogy thought,we may the double integralexplains for the density for plane thin steel plate quality The triple integralexplains for the density for spatial physique quality The curvilinear integralexplains for the density for pole quality The surface integral explains for the density for curved surface thinsteel plate quality Moreover, we also must Newton - the Leibniz formula, the greensformula, the Gaussformula, a stoke formula carry on analogy If we Newton - the Leibniz formula explanation are, it has established a circular function in a sector definite integral if theprimary function in the sector boundary (two spots) between valuerelation Through analogy we may the greens formula explanation be, it has established the dual function in plane region D if theprimary function in the region boundary between on dimorphismcurvilinear integral relation, says from this significance, thegreens formula may regard as Newton - the Leibniz formulatwo-dimensional promotion Through analogy, we may the Gaussformula explanation be, it has established three circular functions in the spatial region if the primary function in between the region boundary dimorphismsurface integral relation, says from this significance, theGaussformula may regard as Newton - the Leibniz formula threedimensional promotion文积分establishedeeting is pes, y Through analogy，The explanation is, it has established three circular functionson space-like surface S dimorphism surface integrals if the primaryfunction in between the S boundary curve dimorphism curvilinearintegral relation, says from this significance, a stoke formula mayregard as Newton - Leibniz formula one kind of high Uygur to promote Through above analogy, we not only promulgated the greens formula,the Gaussformula, the stoke formula common ground are, they have allproduced the spatial some physique integral if in the boundaryintegral relations, they all were allowed to regard as Newton - theLeibniz formula promotion, thus caused between we more furtherunderstanding them the inner link, moreover also has raised ouranalogy thought The practice proved that, in the study, from thefamiliar knowledge, expanded the concept through analogy which newgoods come into the market, new theory, not only is easy to accept,the understanding, to grasp heavily is advantageous to raisesstudents analogy thought, develops its creation ability The analogy thought is creatively the expression thought important method, in thestudy process like can appropriate application analogy, have to beable to receive the twice the result with half the effort studyeffect, we must be positive in the higher mathematics study, utilizeon own initiative 二、 Negative thinking in mathematics application The negative thinking is opposite to the custom thought another kindof thought form Its essential feature is, from had the mentality thereversed direction to ponder the question Along pushes not good,considered counter pushes; The direct solution is not good, thinks themeans indirect solution; After the proposition studies has studied theinverse proposition; When the discussion possibility has thedifficulty, The negative thinking to the open mentality, solves certain difficultproblems, can play the vital role One： if meets certain questions along to push not good, may considercounter pushes Uses when counter pushes the proof question in the higher mathematicshas the widespread application For example, with defines thecertificate function the limit is a difficulty, regarding which wilfully assigns, did not know how begins to look for corresponding 0, in fact, in order to look for the correspondence, the key isutilizes counter pushes and the union solution inequality If proved that, then uses counter to push and the union solution inequality usefollowing step: Regarding0which wilfully assigns 0, for causes the establishment,only needs, therefore may take, Thus may result in to wilfully, at that time, had theestablishment, therefore proved. Also like west the Lagrange theorem of mean and the tan oak thetheorem of mean, is in the differential calculus two fundamentaltheorems These two theorems proof, usually rolls the theorem to taketheir lemma, proved the key all lies in wants a structure auxiliaryfunction to cause it satisfiedly to roll the theorem the condition, wemay use the method which counter pushes to obtain the auxiliaryfunction Presently separately summarizes as follows: Lagrange theorem of mean: If the function satisfies: 1, in continuously, 2, in may lead, Then at least exists causes. With counter pushes the step as follows: Wants the card, onlymust prove, Must cause this type,onlyneed life May confirm this function to have satisfiedly to roll thetheorem three conditions, thus at least exists causes. Two： if encounters certain question direct solution difficulties,thinks the means indirect solution. Regarding this, only lifts two examples to state The example one： tries the card: The analysis if directly strives for very difficultly, however, we usethe indirect method, namely transforms for the judge