摘要:

This paper consists of two parts, appearing in consecutive issues of this journal. It deals with some of the many aspects of modelling physical systems in terms of differential equations (DE), ordinary and partial. Among the issues touched upon are (a) the important role played by the assumptions underlying a DE based mathematical model (Part I), and (b) the interplay between modelling and simulation when using differential equation models (Part II). In a more philosophical vein, there is a section on determinism as well as one on model validation; while fairly general in scope, the concepts examined therein are introduced in direct relation to DE models.

ISSN:0020-739X    

DOI:10.1080/0020739890200501

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Before the turn of the century, to be precise in the 1980s, school mathematics in the developing countries will undergo some changes. This paper therefore enumerates the problems likely to be faced within this period by these countries.

ISSN:0020-739X    

DOI:10.1080/0020739890200502

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

In this article we introduce the notion of ‘cyclic matrices’. Note that the ‘diagonal cyclic matrices’ are a particular case of this one. Cyclic matrices have the property that their product is again a cyclic matrix, and this property is employed in order to solve, in the set of integers, the most important Diophantine equations, as we show with several examples.

ISSN:0020-739X    

DOI:10.1080/0020739890200503

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Analytical results are reported on magneto‐thermoelastic coupled wave propagation in a solid medium. The relevant frequency equations have been obtained by solving equations of elasticity, taking into account the effects of thermal field, magnetic field and the electromagnetic equations of Maxwell. The nature of frequency has been discussed in different cases. It is also shown that, if the frequency is sufficiently smaller than a certain critical frequency, the attenuation factor as well as the phase velocity retain the same characteristics as in a purely thermoelastic body, provided the thermoelastic coupling factor is suitably increased.

ISSN:0020-739X    

DOI:10.1080/0020739890200504

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This paper describes an exploratory investigation of the use of an adaptation of Bloom's taxonomy to classify and compare mathematics questions and papers on the basis of the questions alone. It starts with some background comments on the secondary level public examination system in England and Wales. A critical review of classification schemes for mathematics questions, including a detailed discussion of Bloom's taxonomy, is then given, and this is followed by examples of how a suggested version of Bloom's taxonomy might be used in analysing General Certificate of Education Ordinary level Mathematics papers. Some recommendations for further research are contained in the conclusions section.

ISSN:0020-739X    

DOI:10.1080/0020739890200505

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The aims of this study were (a) to measure the extent of the acquisition of basic mathematical skills encountered in the mathematics curriculum of the elementary, preparatory, and scientific track secondary educational stages in Jordan by students who completed each of these stages at the end of the school year 1984/85, and (b) to determine the effects of the educational stages on the development of basic mathematical skills of students proceeding from one educational stage to another. One hundred and forty‐eight students completed the elementary stage, 273 students completed the preparatory stage, 432 students completed the scientific track secondary stage, 91 students completed second year junior college, and 54 students completed fourth year university at the end of the school year 1984/85.

ISSN:0020-739X    

DOI:10.1080/0020739890200506

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This paper aims at presenting a systematic (historical) account of several interesting classes of convergent series whose sums have received considerable attention in recent works.

ISSN:0020-739X    

DOI:10.1080/0020739890200507

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The Horner algorithm is important and useful for a variety of problems involving polynomial functions. On a practical level, it is the most efficient method for evaluation of polynomials, in the sense of requiring the fewest arithmetic operations. For use in a computer this feature not only saves time, but minimizes the opportunity for propagation of round‐off error. On a more formal level, the Horner algorithm turns out to be virtually equivalent to the procedure of synthetic division of polynomials, in the sense that the same steps used to perform one task also performs the other. This again has practical consequences. It allows us to find a quotient polynomial ‘for free’ in the process of evaluating a polynomial. Finally, since the Newton method for finding zeros of a polynomial involves nothing more complicated than finding the value of a polynomial at a point and then finding the value of the derivative of the polynomial at that point (which itself can be accomplished by another polynomial evaluation!), the Newton method itself can be programmed (to work for polynomials) by making suitable simple additions to a program for the Horner algorithm.

ISSN:0020-739X    

DOI:10.1080/0020739890200508

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

In this paper, the functions which are solutions of constant coefficient homogeneous linear differential (or difference) equations are characterized in terms of the vector space spanned by the set of their translates. For this, a result about the differentiable character of the continuous solutions of Polya's functional equation is used.

ISSN:0020-739X    

DOI:10.1080/0020739890200509

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

For an investment with annually compounded interest the time required for it to double can be quickly estimated by using the ‘rule of 72’ (years to double = 72/percent annual interest). A simple derivation for the rule and an evaluation of its accuracy are presented. Results indicate the rule errs by less than l1/2 months for interest rates between 6 and 12 per cent, and by less than 21/2 months for rates between 5 and 21 per cent, and by less than 31/2 months for 4‐3 per cent or any larger rate.

ISSN:0020-739X    

DOI:10.1080/0020739890200510

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor