Mathematics in Engineering Research

1952 ◽  
Vol 45 (5) ◽  
pp. 331-339
Author(s):  
Chas. M. Cooper

The subject for this evening's talk no doubt calls to mind such things as vector analysis, wave mechanics, Bessel functions, differential equations, matrix algebra, analog computers, and the theory of relativity. I hope you will not be disappointed if such subjects, important though they be, are not mentioned again this evening. I have no intention of belittling these tools of higher mathematics and of theoretical physics. They have their place and it's an important one; but, in engineering research as in most other phases of living, mast progress toward understanding is made through clear, quantitative thinking, employing the simpler mathematical tools taught in elementary and high schools and in the first year or two of college work. So it will be arithmetic rather than analog computers this evening.

1970 ◽  
Vol 5 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Stanley Goldberg

It is a matter of record that Henri Poincaré never responded publicly to Einstein's Special Theory of Relativity (RT). Since almost no private papers of Poincaré are available, his attitude toward Einstein's work and his silence on that score become somewhat of a mystery. It is almost certain that Poincaré knew of Einstein's work in RT. First, he was fluent in German, having learned it as a young man when the Germans occupied his home town of Nancy in 1870. Second, he often reported to the members of the Académie des Sciences on current work in electrodynamics in Germany. It is highly improbable that he would have missed the abstract of Einstein's first paper on RT or the subsequent articles by Einstein on the subject, especially those which were translated into French, since they were in areas directly related to his own interests in theoretical physics.


1911 ◽  
Vol 4 (1) ◽  
pp. 13-20
Author(s):  
Arthur Whipple Smith

I feel that I should explain to you that my acquaintance with the work of the secondary schools is entirely second hand and it may be that my ideas on the subject of graphics in secondary work are colored by what I may wish were possible instead of being entirely true to the facts. In my own experience as an instructor of freshmen I have found but little evidence indicating previous instruction in graphics and frequently the subject is thrust suddenly upon a freshman by the immediate needs of his college work. In many cases it is looked upon as only another novelty introduced to make college mathematics a thing to be dreaded and avoided if possible. I assume that it is proper for an instructor in first-year college work to expect a greater or less degree of familiarity with graphics on the part of incoming students and from this standpoint consider the question as to what may be gained by the study of graphics in connection with all branches of elementary mathematics. The subject should appeal to teachers of mathematics for at least three reasons, first, it is the simplest of our many symbolisms for magnitudes and in the order of nature precedes all the others: second, it often appeals to certain pupils who would otherwise be uninterested: third it affords connecting links among all branches of mathematics.


2008 ◽  
Vol 54 ◽  
pp. 401-424 ◽  
Author(s):  
Petros S. Florides

John Lighton Synge was arguably the greatest Irish mathematician and theoretical physicist since Sir William Rowan Hamilton(1806–65). He was a prolific researcher of great originality and versatility, and a writer of striking lucidity and ‘clarity of expression'. He made outstanding contributions to a vast range of subjects, and particularly to Einstein's theory of relativity. His approach to relativity, and theoretical physics in general, is characterized by his extraordinary geometrical insight. In addition tobringing clarity and new insights to relativity, his geometrical approach profoundly influenced the development of the subject since the 1960s. His crusade in his long academic career was ‘to make space–time a real workshop for physicists, and not a museum visited occasionally with a feeling of awe‘ (31)*.


Author(s):  
Rahmat Nasution And Rahmah

The objective of this research is to find out whether the application Preview, Read,Write, and Recite (PRWR) method improve student’s achievement in readingrecount text. This research applied classroom action research model. This studywas done in six meetings. The subject of this study was first year of SMAN 1Delitua. Primary data were collected by giving 20 questions of multiple-choicetest, the aspects contained in the tests focused on generic structure, main ideas,factual information, and Secondary data were collected by (interview, observationsheet, and questionnaire sheet. Based on analysis data, it was found that thestudent’s achievement improved. It could be seen from the comparison of result inthe orientation test and the cycle test I and II. There were only 9 students who hadpassed minimum criteria KKM in orientation test (75). The improvement showedthat in cycle I and II, based on the total average score it was 16 (42,4%) up to 26(78,7%) in cycle II, The secondary data gathered from interview, observationsheet, and questionnaire sheet, showed that students’ expression and enthusiasticalso improved. Thus, it was found that the applications of Preview, Read, Write,and Recite (PRWR) method in process of teaching improved students’achievement in reading recount text. It is suggested that English teachers applyPRWR method in teaching reading recount text.


2000 ◽  
Vol 421 ◽  
pp. 1-14 ◽  
Author(s):  
HERBERT E. HUPPERT

George Batchelor was one of the giants of fluid mechanics in the second half of the twentieth century. He had a passion for physical and quantitative understanding of fluid flows and a single-minded determination that fluid mechanics should be pursued as a subject in its own right. He once wrote that he ‘spent a lifetime happily within its boundaries’. Six feet tall, thin and youthful in appearance, George's unchanging attire and demeanour contrasted with his ever-evolving scientific insights and contributions. His strongly held and carefully articulated opinions, coupled with his forthright objectivity, shone through everything he undertook.George's pervasive influence sprang from a number of factors. First, he conducted imaginative, ground-breaking research, which was always based on clear physical thinking. Second, he founded a school of fluid mechanics, inspired by his mentor G. I. Taylor, that became part of the world renowned Department of Applied Mathematics and Theoretical Physics (DAMTP) of which he was the Head from its inception in 1959 until he retired from his Professorship in 1983. Third, he established this Journal in 1956 and actively oversaw all its activities for more than forty years, until he relinquished his editorship at the end of 1998. Fourth, he wrote the monumental textbook An Introduction to Fluid Dynamics, which first appeared in 1967, has been translated into four languages and has been relaunched this year, the year of his death. This book, which describes the fundamentals of the subject and discusses many applications, has been closely studied and frequently cited by generations of students and research workers. It has already sold over 45 000 copies. And fifth, but not finally, he helped initiate a number of international organizations (often European), such as the European Mechanics Committee (now Society) and the biennial Polish Fluid Mechanics Meetings, and contributed extensively to the running of IUTAM, the International Union of Theoretical and Applied Mechanics. The aim of all of these associations is to foster fluid (and to some extent solid) mechanics and to encourage the development of the subject.


Author(s):  
Moataz H. Emam

This book is an introduction to the modern methods of the general theory of relativity, tensor calculus, space time geometry, the classical theory of fields, and a variety of theoretical physics oriented topics rarely discussed at the level of the intended reader (mid-college physics major). It does so from the point of view of the so-called principle of covariance; a symmetry that underlies most of physics, including such familiar branches as Newtonian mechanics and electricity and magnetism. The book is written from a minimalist perspective, providing the reader with only the most basic of notions; just enough to be able to read, and hopefully comprehend, modern research papers on these subjects. In addition, it provides a (hopefully short) preparation for the student to be able to conduct research in a variety of topics in theoretical physics; with particular emphasis on physics in curved spacetime backgrounds. The hope is that students with a minimal mathematical background in calculus and only some introductory courses in physics may be able to study this book and benefit from it.


1980 ◽  
Vol 91 ◽  
pp. 261-261
Author(s):  
K. V. Sheridan

A paper that has considerable relevance of the subject matter of this symposium is the following: “Evidence for Extreme Divergence of Open Field Lines from Solar Active Regions,” by G. A. Dulk (Division of Radiophysics, CSIRO, Sydney, Australia and Department of Astro-Geophysics, University of Colorado, Boulder, Colorado), D. B. Melrose (Department of Theoretical Physics, University of Sydney, Australia) and S. Suzuki (Division of Radiophysics, CSIRO, Sydney, Australia).


2000 ◽  
Vol 24 (1) ◽  
pp. 51-55 ◽  
Author(s):  
S P Rao ◽  
S E DiCarlo

Peer instruction is a cooperative-learning technique that promotes critical thinking, problem solving, and decision-making skills. Benson's think-pair-share and Mazur's peer-instruction techniques are simple cooperative exercises that promote student's participation in class and increase student's interaction with each other and with the instructor in a large classroom. We borrowed concepts from Benson and Mazur and applied these concepts to enhance student involvement during the respiratory component of the medical physiology class. The medical physiology class consisted of 256 first-year medical students. The peer-instruction technique was used for 10 classes. Each class of 50 min was divided into three or four short presentations of 12-20 min. Each presentation was followed by a one-question, multiple-choice quiz on the subject discussed. Questions ranged from simple recall to those testing complex intellectual activities. Students were given 1 min to think and to record their first answer. Subsequently, students were allowed 1 min to discuss their answers with their classmates and possibly correct their first response. The percentage of correct answers increased significantly (P < 0.05) after discussion for both recall and intellectual questions. These data demonstrate that pausing three to four times during a 50-min class to allow discussion of concepts enhanced the students level of understanding and ability to synthesize and integrate material.


1928 ◽  
Vol 24 (4) ◽  
pp. 501-505 ◽  
Author(s):  
J. M. Whittaker

In two recent papers Dirac has shown how the “duplexity” phenomena of the atom can be accounted for without recourse to the hypothesis of the spinning electron. The investigation is carried out by the methods of non-commutative algebra, the wave function ψ being a matrix of the fourth order. An alternative presentation of the theory, using the methods of wave mechanics, has been given by Darwin. The four-rowed matrix ψ is replaced by four wave functions ψ1, ψ2, ψ3, ψ4 satisfying four linear differential equations of the first order. These functions are related to one particular direction, and the work can only be given invariance of form at the expense of much additional complication, the four wave functions being replaced by sixteen.


2016 ◽  
Vol 26 (65) ◽  
pp. 377-385 ◽  
Author(s):  
Soledad Carretero Pérez ◽  
Silvia Ana Español

Abstract An interpretative review of research on adult-infant interactions involving the analysis of movement behaviors is presented, systematically linking previous studies to current research on the subject. Forty-two articles analyzing the dyad's interactive movement in the period 1970-2015 were found. Twelve papers were excluded, including only those that studied the phenomenon in the baby's first year of life. The results revealed that movement was a central topic in early interaction studies in the 70s. In the 1980's and 1990's, its study was marginal and it is currently resurging under the embodiment perspective. The conceptual framework and research methods used in the pioneering work are presented, and the thematic foci shared with current research are highlighted. Thus, essential keys are provided for the updated study of early interactions from a multimodal perspective.


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