The Role Of Mathematics In Physical Sciences
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Mathematics And The Natural Sciences
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Author : Francis Bailly
language : en
Publisher: World Scientific
Release Date : 2011
Mathematics And The Natural Sciences written by Francis Bailly and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
The book aims at the identification of the organising concepts of some physical and biological phenomena, by means of an analysis of the foundations of mathematics and of physics. This is done in the perspective of unifying phenomena, of bringing different conceptual universes into dialog. The analysis of the role of “order” and of symmetries in the foundations of mathematics is linked to the main invariants and principles, among which the geodesic principle (a consequence of symmetries), which govern and confer unity to the various physical theories. Moreover, we attempt to understand causal structures, a central element of physical intelligibility, in terms of symmetries and their breakings. The importance of the mathematical tool is also highlighted, enabling us to grasp the differences in the models for physics and biology which are proposed by continuous and discrete mathematics, such as computational simulations. A distinction between principles of (conceptual) construction and principles of proofs, both in physics and in mathematics, guides this part of the work.As for biology, being particularly difficult and not as thoroughly examined at a theoretical level, we propose a “unification by concepts”, an attempt which should always precede mathematisation. This constitutes an outline for unification also basing itself upon the highlighting of conceptual differences, of complex points of passage, of technical irreducibilities of one field to another. Indeed, a monist point of view such as ours should not make us blind: we, the living objects, are surely just big bags of molecules or, at least, this is our main metaphysical assumption. The point though is: which theory can help us to better understand these bags of molecules, as they are, indeed, rather “singular”, from the physical point of view. Technically, this singularity is expressed by the notion of “extended criticality”, a notion that logically extends the pointwise critical transitions in physics.
The Role Of Mathematics In Physical Sciences
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Author : Giovanni Boniolo
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-22
The Role Of Mathematics In Physical Sciences written by Giovanni Boniolo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-22 with Science categories.
Even though mathematics and physics have been related for centuries and this relation appears to be unproblematic, there are many questions still open: Is mathematics really necessary for physics, or could physics exist without mathematics? Should we think physically and then add the mathematics apt to formalise our physical intuition, or should we think mathematically and then interpret physically the obtained results? Do we get mathematical objects by abstraction from real objects, or vice versa? Why is mathematics effective into physics? These are all relevant questions, whose answers are necessary to fully understand the status of physics, particularly of contemporary physics. The aim of this book is to offer plausible answers to such questions through both historical analyses of relevant cases, and philosophical analyses of the relations between mathematics and physics.
Mathematics In Physics Education
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Author : Gesche Pospiech
language : en
Publisher:
Release Date : 2019
Mathematics In Physics Education written by Gesche Pospiech and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.
This book is about mathematics in physics education, the difficulties students have in learning physics, and the way in which mathematization can help to improve physics teaching and learning. The book brings together different teaching and learning perspectives, and addresses both fundamental considerations and practical aspects. Divided into four parts, the book starts out with theoretical viewpoints that enlighten the interplay of physics and mathematics also including historical developments. The second part delves into the learners' perspective. It addresses aspects of the learning by secondary school students as well as by students just entering university, or teacher students. Topics discussed range from problem solving over the role of graphs to integrated mathematics and physics learning. The third part includes a broad range of subjects from teachers' views and knowledge, the analysis of classroom discourse and an evaluated teaching proposal. The last part describes approaches that take up mathematization in a broader interpretation, and includes the presentation of a model for physics teachers' pedagogical content knowledge (PCK) specific to the role of mathematics in physics.
Mathematics For The Physical Sciences
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Author : Herbert S Wilf
language : en
Publisher: Courier Corporation
Release Date : 2013-01-18
Mathematics For The Physical Sciences written by Herbert S Wilf and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-18 with Mathematics categories.
Topics include vector spaces and matrices; orthogonal functions; polynomial equations; asymptotic expansions; ordinary differential equations; conformal mapping; and extremum problems. Includes exercises and solutions. 1962 edition.
Student Solution Manual For Foundation Mathematics For The Physical Sciences
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Author : K. F. Riley
language : en
Publisher: Cambridge University Press
Release Date : 2011-03-28
Student Solution Manual For Foundation Mathematics For The Physical Sciences written by K. F. Riley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-28 with Science categories.
This Student Solution Manual provides complete solutions to all the odd-numbered problems in Foundation Mathematics for the Physical Sciences. It takes students through each problem step-by-step, so they can clearly see how the solution is reached, and understand any mistakes in their own working. Students will learn by example how to arrive at the correct answer and improve their problem-solving skills.
Mathematical Physics
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Author : Francis Bitter
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
Mathematical Physics written by Francis Bitter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
Reader-friendly guide offers illustrative examples of the rules of physical science and how they were formulated. Topics include the role of mathematics as the language of physics; nature of mechanical vibrations; harmonic motion and shapes; geometry of the laws of motion; more. 60 figures. 1963 edition.
Mathematics For The Physical Sciences
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Author : Laurent Schwartz
language : en
Publisher: Courier Dover Publications
Release Date : 2008-04-21
Mathematics For The Physical Sciences written by Laurent Schwartz and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-21 with Mathematics categories.
Concise treatment of mathematical entities employs examples from the physical sciences. Topics include distribution theory, Fourier series, Laplace transforms, wave and heat conduction equations, and gamma and Bessel functions. 1966 edition.
Mathematics For Physics
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Author : Michael Stone
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-09
Mathematics For Physics written by Michael Stone and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-09 with Science categories.
An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.
Mathematics For Physics
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Author : Michael M. Woolfson
language : en
Publisher: Oxford University Press
Release Date : 2007
Mathematics For Physics written by Michael M. Woolfson and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Mathematics for Physics features both print and online support, with many in-text exercises and end-of-chapter problems, and web-based computer programs, to both stimulate learning and build understanding.
Mathematics And Science
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Author : Ronald E Mickens
language : en
Publisher: World Scientific
Release Date : 1990-08-23
Mathematics And Science written by Ronald E Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-08-23 with Mathematics categories.
The purpose of this review volume is to present the opinions of a number of distinguished individuals who have given careful thought as to why mathematics is so “unreasonably effective” when applied to the analysis of the natural sciences.