摘要:

The limit‐cycle solution of van der Pol's non‐linear differential equation is found approximately by the method of perturbation; this is suitable when the non‐linearity is weak. At each stage of the perturbation a linear differential equation is solved and two unknown constants of integration arise. The text‐books usually determine these constants by specifying zero initial conditions for the perturbation and its derivative. This procedure cannot be justified when finding a limit‐cycle of a non‐linear differential equation and it leads to some wrong values. The method used here is to choose the constants of integration so as to minimize the residual error when the truncated solution is substituted in the differential equation. It is then found that each perturbation depends upon the position of truncation. Numerical values are given for truncation at the first and second perturbations.

ISSN:0020-739X    

DOI:10.1080/0020739750060211

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

Starting from the differential equation describing the path of a photon in the Schwarzschild field of a spherically symmetric non‐rotating star in empty space we derive the condition for the light emitted from such a star to return to its surface, and describe some features of its orbit. The principal results are(a)only stars of radius < 1‐5 (in units of the Schwarzschild radius) can recapture their photons,(b)no photon which is ultimately recaptured goes further than 1 ‐5 units from the centre of the star, (c) provided the stellar radius is <l‐5 the angular diameter of the star as seen by a distant observer isindependentof that radius.

ISSN:0020-739X    

DOI:10.1080/0020739750060212

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

Questions of educational and statistical validity raised by multiple assessment techniques are examined in terms of educational objectives, errors and distributions of scores. A method of scaling is proposed and its relation to normalizing procedures discussed in recent papers in this journal is indicated. A hypothetical situation provides the framework for the elaboration of the ideas presented.

ISSN:0020-739X    

DOI:10.1080/0020739750060213

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

摘要:

A technique is discussed by which a simple analogue computer can be simulated in a programming language like Fortran. This helps to improve students’ understanding of the structure and solution of a differential equation. Its advantage is in its simplicity of usage and availability for machines of all sizes.

ISSN:0020-739X    

DOI:10.1080/0020739750060214

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739750060215

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739750060216

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor

ISSN:0020-739X    

DOI:10.1080/0020739750060217

出版商:Taylor & Francis Group    

年代:1975

数据来源: Taylor