摘要:

This article contains a discussion of Euler's buckling formula for a compressed elastic column. The most commonly used classroom derivations of this formula follow roughly the original arguments of Euler. For this reason the history of this problem is briefly reviewed. Alternative methods of derivation use energy arguments, including Rayleigh's principle and Kirchhof's energy inequality.

ISSN:0020-739X    

DOI:10.1080/0020739830140601

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This paper derives Leibniz's rule with n = ‐1 and shows that it may be used to simplify extended integration by parts in certain examples which occur in the derivation of Fourier series. A simple derivation of the general Taylor expansion with integral remainder form is also obtained.

ISSN:0020-739X    

DOI:10.1080/0020739830140602

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This paper considers the role that mathematics plays in the teaching of home economics at secondary school. A syllabus and teaching approach for student teachers is presented. Similar ideas could be developed in other subject areas.

ISSN:0020-739X    

DOI:10.1080/0020739830140603

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This article deals with the distributions of the sum, the product and the quotient of two generalized bivariate chi‐square variates by first suggesting a generalization of a bivariate chi‐square distribution.

ISSN:0020-739X    

DOI:10.1080/0020739830140604

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Thousands of candidates submit themselves to computer‐scored examinations annually. Whilst the great majority of these are controlled by external examining boards, an important portion involve undergraduate and postgraduate medical examinations in which there is little review of the effects of the scoring schemes used. This particularly applies where such question papers require the identification of false as well as true alternatives.

ISSN:0020-739X    

DOI:10.1080/0020739830140605

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The principle and construction of common‐log extension tables for complex numbers are described. These tables are to be used in conjunction with real log tables for performing complex arithmetic. This method is many times faster than the conventional polar‐form method for manual computation using pocket calculators.

ISSN:0020-739X    

DOI:10.1080/0020739830140606

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Three modelling excercises from microeconomics are presented, both as examples of a methodology for teaching economics to mathematically inclined students, and as a vehicle for teaching modelling as a general skill. The first exercise, a price adjustment model for perfect competition, is given in detail within a formulation/solution/generalization/validation scheme with suggestions for an interactive teaching strategy. The results of giving the exercise to a second‐year BSc class in Mathematics and Computing are reported. Outlines of two further exercises relating to oligopoly and related models are given, and an Appendix provides a series of graduated problems for the first of these exercises.

ISSN:0020-739X    

DOI:10.1080/0020739830140607

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This model assumes three separate investors each with a set amount of money. The full amount is to be invested in six investments, namely: long‐term bonds, short‐term bonds, treasury bonds, common stock, treasury bills, and commercial paper. The investment is made according to weights assigned to safety of principal, growth, current income, taxable income and volatility. The weights are derived by obtaining pairwise comparison matrices and then using an averaging process.

ISSN:0020-739X    

DOI:10.1080/0020739830140608

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

An elementary analysis of the problem of tides on an ideal Earth from a point of view of the forces involved proves to be a valuable exercise in terms of the applied mathematics as well as the physics. The approximations show their value both for obtaining analytic solutions and for exhibiting the symmetry‐breaking at higher order.

ISSN:0020-739X    

DOI:10.1080/0020739830140609

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

If l alternative responses are provided for each of n equally‐weighted questions in a multiple‐choice examination, and the candidate correctly indicates t answers, the prior probability estimate of the number of answers actually known is given by (lt – n)/(l – 1), a result implicit in most assessment schemes.

ISSN:0020-739X    

DOI:10.1080/0020739830140610

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor