ISSN:0020-739X    

DOI:10.1080/0020739950260101

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We describe the implementation of a computer‐supported individual self‐study system in a second‐year course for students computer science. We give information on the educational software that has been developed and we present details of our method of evaluation. The main goal of the project was to design an educational tool that forces students to work regularly and on scheme. We will show that we have succeeded in this objective.

ISSN:0020-739X    

DOI:10.1080/0020739950260102

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The development and evaluation of a computer package for teaching mathematics to 6‐7‐year‐old pupils is presented. The package consists of six computer programs followed by worksheets and teaching guides and covers basic mathematical concepts met in the school curriculum. It aims to enhance children's understanding of certain concepts and structures, help them to develop and communicate problem‐solving strategies, stimulate interest and provide a variety of learning environments. The programs mainly present one teaching point and vary from rather structured ones to ‘open’ mathematical explorations. The context has been chosen to be familiar to the children and a variety of representation models has been adopted to facilitate children's understanding. The evaluation is designed to determine the effectiveness of software in terms of the aims stated at the design stage. The programs were used by children moved from their classroom, by a class of 30 children working in groups of three in the computer room and in their normal classroom. Methods used were observation and interviews with children and teacher, whole‐class discussion, and analysis of children's written work. In general, the developed software appeared to fulfil its main goals. It encouraged discussion, problem posing, mathematical explorations that led the children to reflect on their methods and conceptions and develop them.

ISSN:0020-739X    

DOI:10.1080/0020739950260103

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We introduce an ergodic Markov chain in the process of mathematical modelling and through this we obtain some useful conclusions concerning the application of the model building process to the classroom.

ISSN:0020-739X    

DOI:10.1080/0020739950260104

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In this article, we discuss some examples on the use of the theory of analytic functions to construct accurate and efficient quadrature formulas for numerical evaluation of integrals, and also examine the errors incurred associated with some quadrature formulas. Though some integrals treated in this article are real, their behaviours are best understood only if we consider the variables as complex. This is analogous to the example that we can understand why the simple real function 1/(1 + x2) converges for \x\ < 1 only if we move into the complex plane. In the first section, we examine the deterioration of accuracy when the integrand has poles near the interval of integration and we derive appropriate modified quadrature formulas to improve accuracy. The integrals with rational and Poisson-type kernels are discussed as examples. In the second section, we show the derivation of some algorithms which perform the numerical inversion of Laplace transform. Three inversion algorithms are presented, namely, Fourier series expansion method, Laguerre polynomial expansion method and kernel approximation method. Inherent difficulties in numerical Laplace inversion are also discussed.

ISSN:0020-739X    

DOI:10.1080/0020739950260105

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The relation between complex numbers and plane rotations is given. In an effort to extend this relation to space rotations and some generalizations of complex numbers, one is led to Hamilton's quaternions and the group of unitary transformations SU(2). The presentation is inspired by the historical development of the subject and aims at giving a natural formulation of important algebraic concepts, based on the study of mathematically relevant concrete examples.

ISSN:0020-739X    

DOI:10.1080/0020739950260106

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A simplified method is developed following two different approaches, one proposed by Mazumder and other by Banerjee for the analysis of large amplitude transverse vibration of thin, isotropic, homogeneous elastic plates of arbitrary shapes. As an illustration of the method, an interesting example of the vibration of a parabolic plate is examined. Numerical results are presented in tabular form and corresponding graphs are drawn and compared with available results.

ISSN:0020-739X    

DOI:10.1080/0020739950260107

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

There is an increasing expansion of courses in statistics with a large number of students (100 or more) as a result of modularization and semesterization. A different approach is required in teaching and assessment on such large courses which have students of varying entry qualifications. It is argued that the best method for teaching is a traditional lecture for 2 hours followed by a seminar/tutorial. For assessment in large classes a combination of end‐of‐semester/year examination and a group project using computer packages with ‘peer assessment’ is most preferred. For successful use of this method of teaching and assessment, it is necessary to have proper controls and mechanisms for its implementation, otherwise the students are deprived of essential learning benefits.

ISSN:0020-739X    

DOI:10.1080/0020739950260108

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

A class of new (we believe) third‐order formulae for the iterative solution of the equationf(x) =0 are derived. The formulae contain the methods of Chebyshev and Halley as special cases, and some numerical examples are given to demonstrate the convergence behaviour. General formulae of at least fourth‐order are also presented and, in particular, their application to the extraction of roots is illustrated. Apart from the potential for further investigations the study could be used as the theme of a student project on iterative methods for the solution off(x) = 0.

ISSN:0020-739X    

DOI:10.1080/0020739950260109

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The article describes several issues around the so‐called fundamental theorem of algebra.

ISSN:0020-739X    

DOI:10.1080/0020739950260110

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor