摘要:

Undergraduate mathematics is shown to play an important role in research in modern continuum mechanics. Concise examples of analysis are drawn from recent applications to non‐linear heat conduction problems, and it is shown how modern algebra is used in describing material behaviour. The reader is directed to journals and books in which mathematics and continuum mechanics are practically synonymous.

ISSN:0020-739X    

DOI:10.1080/0020739730040301

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

It is shown that a class of planar conjugated hydrocarbon molecules can be modelled in terms of a simple graph and the related adjacency matrix. Various physical and chemical properties are related to properties of the graphs. The resonance energy is related to such simple invariants as the total number of CC links and the number of Kekulé structures. Rules for enumerating these structures are described.

ISSN:0020-739X    

DOI:10.1080/0020739730040302

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

This paper presents a resume of some of the methods and problems encountered in phase‐plane plotting.

ISSN:0020-739X    

DOI:10.1080/0020739730040303

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

Conservation laws in the form of integral invariants of linear systems form a particularly simple concept. This is developed into a teaching tool connecting various other fields with this physical notion in such a way that it may be introduced as a seminal first year topic in applied mathematics.

ISSN:0020-739X    

DOI:10.1080/0020739730040304

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

This paper discusses some of the difficulties encountered by secondary school pupils in working backwards from the raw data which they obtain in their science experiments to mathematical models of relations which may subsist in the data. An example from school chemistry is discussed, and an analysis is attempted of the skills required in going from experimental results to final conclusion.

ISSN:0020-739X    

DOI:10.1080/0020739730040305

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

The need to examine the average, the standard deviation and the distribution of a set of raw examination marks is discussed.

ISSN:0020-739X    

DOI:10.1080/0020739730040306

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

A survey is given of the various methods of determining the slope and intercept of a straight line when both variables are subject to error. The results for each method, after one iteration, are compared with the best available computer method by analysing 100 sets of data. A procedure suitable for use on a calculating machine is recommended in which the gradient differs from the best value by some 3‐4 per cent of its standard error for the 100 sets of data considered.

ISSN:0020-739X    

DOI:10.1080/0020739730040307

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

The present paper outlines some basic principles upon which an outlook in teaching and research in mathematics in educational institutions can be developed. Definingapplied mathematics,the author analyses the basic topics of mathematics which permeate throughout the wider fields and diversified aspects of this branch of mathematical science.

ISSN:0020-739X    

DOI:10.1080/0020739730040308

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

In this article a pattern arising from the coefficients in the expansion of the sum of the ≪th powers of the roots of a quadratic equation is explored by computer. The paper is presented in the form of a correspondence on this problem, which originated during the Computer Appreciation Course held in University College, Galway, in July 1971, for teachers of mathematics for sixth forms. It is felt that the use of the conversational mode may emphasize some of the points of educational interest which arise in the elementary FORTRAN IV programs which are used to generate the array of coefficients. Two methods are adopted: the first involving a direct calculation using binomial coefficients and the second utilizing a recurrence relation. The programs are deliberately unsophisticated so that the educational aspects of the comparison of the methods may be high‐lighted.

ISSN:0020-739X    

DOI:10.1080/0020739730040309

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

From the bulk or non‐particle laws of motion, work‐energy relations of mechanics are derived in a manner which does not require the introduction of the concept of internal force. The rotational motion work‐energy equation is then specialized to the case of a rigid body. Next internal forces are introduced and a conservation of mechanical energy expression is developed.

ISSN:0020-739X    

DOI:10.1080/0020739730040310

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor