共查询到20条相似文献,搜索用时 15 毫秒
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《中学生数学》2014,(13)
<正>An equation involving a derivative is called a differential equation.Such as,(dy)/(dx)=2x,and the function y=f(x)satisfies this equation.When we know the additional condition that y=2when x=-1,the function y=f(x)will be find exactly.The additional condition is called the initial condition.It is used to evaluate constant of integration. 相似文献
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When I learned the following basic formula of indefinite integrals in the calculus,at that time I was a teenager,the strange ideas had jump out my head.I would be a great girl in math if I can change all the ? in the following formula to the real functions 相似文献
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<正>In this paper you will learn the basic integration rule from the basic differentiation rule.Last time we have learned anti-derivative,indefinite integral,and the power rule in integration.Let us recall what the power rule in differentiation is.If n is a real number,and y=xn,then y'=nxn-1.Proof:Let y=xn,we get ln|y|=ln|xn|,Since ln|xn|=n ln|x|,so we get ln|y|=n ln|x|.Take differentiation for both side above:y'y=n x. 相似文献
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The anti-derivative or indefinite integral of a function f(x)is a function F(x)whose derivative is f(x).Then,each differentiation rule should have a corresponding integration rule.Last time we worked with the substitution rule for integration corresponds to the chain rule in differentiation.What is 相似文献
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This paper presents the results of interviews with 174 participants solving a problem of elementary mathematics, connected with the part–whole approach to fractions. The motive for the investigation was a specific kind of difficulty observed during a case study conducted to verify the elementary school student's understanding of the concept of fractions. The authors decided to examine the problem in a broader population of mathematics learners at different levels of education: from elementary school to university students and graduates of science majors. Approximately 65% of respondents reported the wrong answer immediately after reading the fraction problem taken from the fourth grade of elementary school. Detailed analysis of the respondents’ performance showed that the source of many wrong answers was a false belief about fractions: The only way to get 1/n of a given whole is to divide this whole into n equal parts, not yet described in educational literature. 相似文献
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《中学生数学》2014,(19)
<正>1.What a rational function?Do you remember what a polynomial function is?If you know a function of the form is a form as following f(x)=anxn+an-ixn-1+...+a1x+a0,where an,an-i,...a1,a0are real numbers and nis nonnegative integer.The domain of a polynomial function is the set of all real numbers.But here are some func- 相似文献
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Carl de Boor 《BIT Numerical Mathematics》2001,41(5):880-890
A formula is given for the inverse of the linear map, from coordinate space to a linear space, induced by a basis for that linear space, which is then connected to various basic Applied Linear Algebra constructs.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
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《Chaos, solitons, and fractals》2000,11(12):1827-1834
The role of stochastic resonance (SR) in the detection of signals is discussed. It is shown that when a signal is not detectable using traditional methods, such as spectral analysis or averaging, it cannot be detected using SR. In other words by adding noise a far-from detectable signal cannot become detectable. 相似文献
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Victoria Gitman Joel David Hamkins Thomas A. Johnstone 《Mathematical Logic Quarterly》2016,62(4-5):391-406
We show that the theory , consisting of the usual axioms of but with the power set axiom removed—specifically axiomatized by extensionality, foundation, pairing, union, infinity, separation, replacement and the assertion that every set can be well‐ordered—is weaker than commonly supposed and is inadequate to establish several basic facts often desired in its context. For example, there are models of in which ω1 is singular, in which every set of reals is countable, yet ω1 exists, in which there are sets of reals of every size , but none of size , and therefore, in which the collection axiom fails; there are models of for which the ?o? theorem fails, even when the ultrapower is well‐founded and the measure exists inside the model; there are models of for which the Gaifman theorem fails, in that there is an embedding of models that is Σ1‐elementary and cofinal, but not elementary; there are elementary embeddings of models whose cofinal restriction is not elementary. Moreover, the collection of formulas that are provably equivalent in to a Σ1‐formula or a Π1‐formula is not closed under bounded quantification. Nevertheless, these deficits of are completely repaired by strengthening it to the theory , obtained by using collection rather than replacement in the axiomatization above. These results extend prior work of Zarach 18 . 相似文献
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《中学生数学》2017,(21)
<正>Now we'll learn what the alternating series estimation theorem is?A partial sumSnof any convergent series can be used as an approximation to the total sum.If we want estimate the accuracy of approximation,then the error and remainder should be considered.The error involved in using S≈Snis the remainder.In other words,error involved in using 相似文献
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L D Phillips 《The Journal of the Operational Research Society》2011,62(5):926-929
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A continuous process is a person who draws the curve without a break,or,takes place gradually without interruption. Those are a daily language in continuity. However,in calculus,we notice that the limit of a function as x approaches a can often be found simply by calculating the value of the function at a. It means a continuous function 相似文献
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The powerset operator, , is an operator which (1) sends sets to sets,(2) is defined by a positive formula and (3) raises the cardinality of its argument, i.e., |(x)|>|x|. As a consequence of (3), has a proper class as least fixed point (the universe itself). In this paper we address the questions: (a) How does contribute to the generation of the class of all positive operators? (b) Are there other operators with the above properties, independent of ? Concerning (a) we show that every positive operator is a combination of the identity, powerset, and almost constant operators. This enables one to define what a -independent operator is. Concerning (b) we show that every -independent bounded positive operator is not -like.Mathematics Subject Classification (2000): Primary 03E05, secondary 03E20 相似文献
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David Eisenbud Craig Huneke Bernd Ulrich 《Proceedings of the American Mathematical Society》2003,131(3):701-708
In this paper we show that the Rees algebra can be made into a functor on modules over a ring in a way that extends its classical definition for ideals. The Rees algebra of a module may be computed in terms of a ``maximal' map from to a free module as the image of the map induced by on symmetric algebras. We show that the analytic spread and reductions of can be determined from any embedding of into a free module, and in characteristic 0--but not in positive characteristic!--the Rees algebra itself can be computed from any such embedding.
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《中学生数学》2006,(17)
As a child you learned by experimenting with the natural world about you.You learned how to walk.talk,and hold your spoon,all by trial and error.After many tries,you eventually learned how to ride your first bicycle,discovering it was easier to keep your bal- ance if you kept the bike moving.You learned by expe- rience that counterclockwise motion turns on a water faucet and a clockwise motion turns it off.Most of your learning has been by a process called inductive reasoning. 相似文献
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