摘要:

Through a number of examples this paper illustrates the usefulness of dimensional analysis. A brief discussion shows how dimensional analysis can be generalized by studying the invariance of problems under Lie groups of transformations.

ISSN:0020-739X    

DOI:10.1080/0020739830140301

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

At least one student tried to solve a problem of extremum in a matriculation examination in a way which led to the problem of extremum at the endpoint of a curve. He fell into his own trap, but the case calls attention to the fact that we must not forget to teach such situations.

ISSN:0020-739X    

DOI:10.1080/0020739830140302

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Various aspects of the real nonlinear mapping z'= z2— kz + k, where 0 < k ≤ 4, are studied using elementary methods. In particular fixed points and cycles of periods 2 and 3 are examined, and criteria are established for their existence and stability.

ISSN:0020-739X    

DOI:10.1080/0020739830140303

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A network of ten resistors in series and parallel is stated. The network has five switches. The problem is to find the resistor values such that when the switches are set in five different positions, the resistance requirements for the circuit are satisfied. The resultant system of five non‐linear equations in ten unknowns is solved using multi‐stage Monte Carlo.

ISSN:0020-739X    

DOI:10.1080/0020739830140304

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A simple model for cognitive processes will be constructed using the notions of concept image and concept definition. The model will be used to analyse some phenomena in the process of the learning of the function concept in grades 10 and 11. Educational conclusions, similar to those in [3] which were based on historical arguments, will be drawn.

ISSN:0020-739X    

DOI:10.1080/0020739830140305

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This note is concerned with the correct determination of the asymptotic behaviour of the solution at infinity of a second‐order differential equation boundary value problem when one boundary condition is given at infinity.

ISSN:0020-739X    

DOI:10.1080/0020739830140306

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Three tests published by the Mathematics Association of America were administered during the first week of classes to students enrolling in algebra, pre‐calculus algebra, and trigonometry classes. Scores were correlated with grades using eta and Pearson correlations. Eta coefficients were significant for all classes. The Pearson correlations were significant for the two algebra courses but not for the trigonometry course. It was concluded that the algebra tests were valid as predictors of course grade but no support was found for the validity of the trigonometry test.

ISSN:0020-739X    

DOI:10.1080/0020739830140307

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Optimal Portfolio Theory, as developed during the last twenty‐seven years, represents an important application of mathematics to a very useful field and as such should find its proper place in the education of mathematicians, economists, actuaries, business managers, scientists and engineers. The present article gives a tutorial introduction to Markowitz's basic idea of mean‐variance efficient portfolios and his critical‐line method for obtaining them. A new and simpler approach to implementation of critical line method is given. Some ideas from Pareto optimization are used to get a better insight into the theory. Implication of Maximum Expected Utility and other possible criteria are discussed. The last section gives a list of open problems in the field.

ISSN:0020-739X    

DOI:10.1080/0020739830140308

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

An experimental‐optical approach to the teaching of conic sections is presented. This approach has been used successfully for a considerable time with high school pupils and with students taking degree courses in the teaching of mathematics and physics. Mirrors in the form of parabola, ellipse, circle and hyperbola are used to show paths of incident and reflected light. These paths demonstrate the optical characteristics of the mirror curves and some geometrical characteristics of the conic sections. Finally, for completeness as a teaching tool, the string and pencil methods of drawing the conic sections are noted.

ISSN:0020-739X    

DOI:10.1080/0020739830140309

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A student is taught the advantages of adaptive quadrature over traditional numerical integration, but in practice, he cannot verify these for himself because of the complexity involved in programming such algorithms. In an attempt to overcome some of the programming difficulties, various books, see [1, 2], compromise by recommending a restricted number of nested subintervals. However, while such a compromise alleviates the storage problem, it may, in the case of ‘badly‐behaved’ integrands, prove to be too restrictive and thus destroy the concept of adaptive quadrature. This paper introduces an adaptive quadrature algorithm that demands neither storing strategies, nor a preset limit on the number of subdivisions. The algorithm is simple enough to be manipulated by undergraduates. A FORTRAN listing of the algorithm is included in this paper.

ISSN:0020-739X    

DOI:10.1080/0020739830140310

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor