Understanding Mathematical Concepts In Physics

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Understanding Physics Using Mathematical Reasoning

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Author : Andrzej Sokolowski
language : en
Publisher: Springer Nature
Release Date : 2021-08-20

Understanding Physics Using Mathematical Reasoning written by Andrzej Sokolowski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-20 with Education categories.

This book speaks about physics discoveries that intertwine mathematical reasoning, modeling, and scientific inquiry. It offers ways of bringing together the structural domain of mathematics and the content of physics in one coherent inquiry. Teaching and learning physics is challenging because students lack the skills to merge these learning paradigms. The purpose of this book is not only to improve access to the understanding of natural phenomena but also to inspire new ways of delivering and understanding the complex concepts of physics. To sustain physics education in college classrooms, authentic training that would help develop high school students’ skills of transcending function modeling techniques to reason scientifically is needed and this book aspires to offer such training The book draws on current research in developing students’ mathematical reasoning. It identifies areas for advancements and proposes a conceptual framework that is tested in several case studies designed using that framework. Modeling Newton’s laws using limited case analysis, Modeling projectile motion using parametric equations and Enabling covariational reasoning in Einstein formula for the photoelectric effect represent some of these case studies. A wealth of conclusions that accompany these case studies, drawn from the realities of classroom teaching, is to help physics teachers and researchers adopt these ideas in practice.

Understanding Mathematical Concepts In Physics

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Author : Sanjeev Dhurandhar
language : en
Publisher: Springer Nature
Release Date : 2024-07-16

Understanding Mathematical Concepts In Physics written by Sanjeev Dhurandhar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-16 with Science categories.

Modern mathematics has become an essential part of today’s physicist’s arsenal and this book covers several relevant such topics. The primary aim of this book is to present key mathematical concepts in an intuitive way with the help of geometrical and numerical methods - understanding is the key. Not all differential equations can be solved with standard techniques. Examples illustrate how geometrical insights and numerical methods are useful in understanding differential equations in general but are indispensable when extracting relevant information from equations that do not yield to standard methods. Adopting a numerical approach to complex analysis it is shown that Cauchy’s theorem, the Cauchy integral formula, the residue theorem, etc. can be verified by performing hands-on computations with Python codes. Figures elucidate the concept of poles and essential singularities. Further the book covers topology, Hilbert spaces, Fourier transforms (discussing how fast Fourier transform works), modern differential geometry, Lie groups and Lie algebras, probability and useful probability distributions, and statistical detection of signals. Novel features include: (i) Topology is introduced via the notion of continuity on the real line which then naturally leads to topological spaces. (ii) Data analysis in a differential geometric framework and a general description of χ2 discriminators in terms of vector bundles. This book is targeted at physics graduate students and at theoretical (and possibly experimental) physicists. Apart from research students, this book is also useful to active physicists in their research and teaching.

Introduction To Mathematical Physics

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Author : Chun Wa Wong
language : en
Publisher: Oxford University Press, USA
Release Date : 2013-01-24

Introduction To Mathematical Physics written by Chun Wa Wong and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-24 with Science categories.

Introduction to Mathematical Physics explains why and how mathematics is needed in describing physical events in space. It helps physics undergraduates master the mathematical tools needed in physics core courses. It contains advanced topics for graduate students, short tutorials on basic mathematics, and an appendix on Mathematica.

Quirky Quantum Concepts

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Author : Eric L. Michelsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-04

Quirky Quantum Concepts written by Eric L. Michelsen 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 2014-02-04 with Science categories.

Quirky Quantum Concepts explains the more important and more difficult concepts in theoretical quantum mechanics, especially those which are consistently neglected or confusing in many common expositions. The emphasis is on physical understanding, which is necessary for the development of new, cutting edge science. In particular, this book explains the basis for many standard quantum methods, which are too often presented without sufficient motivation or interpretation. The book is not a simplification or popularization: it is real science for real scientists. Physics includes math, and this book does not shy away from it, but neither does it hide behind it. Without conceptual understanding, math is gibberish. The discussions here provide the experimental and theoretical reasoning behind some of the great discoveries, so the reader may see how discoveries arise from a rational process of thinking, a process which Quirky Quantum Concepts makes accessible to its readers. Quirky Quantum Concepts is therefore a supplement to almost any existing quantum mechanics text. Students and scientists will appreciate the combination of conversational style, which promotes understanding, with thorough scientific accuracy.

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.

Explorations In Mathematical Physics

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Author : Don Koks
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-15

Explorations In Mathematical Physics written by Don Koks 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 2006-09-15 with Science categories.

Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.

Physics For Mathematicians

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Author : Michael Spivak
language : en
Publisher:
Release Date : 2010

Physics For Mathematicians written by Michael Spivak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mechanics categories.

An Invitation To Mathematical Physics And Its History

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Author : Jont Allen
language : en
Publisher: Springer Nature
Release Date : 2020-09-22

An Invitation To Mathematical Physics And Its History written by Jont Allen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-22 with Technology & Engineering categories.

This state of the art book takes an applications based approach to teaching mathematics to engineering and applied sciences students. The book lays emphasis on associating mathematical concepts with their physical counterparts, training students of engineering in mathematics to help them learn how things work. The book covers the concepts of number systems, algebra equations and calculus through discussions on mathematics and physics, discussing their intertwined history in a chronological order. The book includes examples, homework problems, and exercises. This book can be used to teach a first course in engineering mathematics or as a refresher on basic mathematical physics. Besides serving as core textbook, this book will also appeal to undergraduate students with cross-disciplinary interests as a supplementary text or reader.

Mathematics For Physicists

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Author : Alexander Altland
language : en
Publisher:
Release Date : 2019

Mathematics For Physicists written by Alexander Altland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematical physics categories.

This textbook is a comprehensive introduction to the key disciplines of mathematics - linear algebra, calculus, and geometry - needed in the undergraduate physics curriculum. Its leitmotiv is that success in learning these subjects depends on a good balance between theory and practice. Reflecting this belief, mathematical foundations are explained in pedagogical depth, and computational methods are introduced from a physicist's perspective and in a timely manner. This original approach presents concepts and methods as inseparable entities, facilitating in-depth understanding and making even advanced mathematics tangible. The book guides the reader from high-school level to advanced subjects such as tensor algebra, complex functions, and differential geometry. It contains numerous worked examples, info sections providing context, biographical boxes, several detailed case studies, over 300 problems, and fully worked solutions for all odd-numbered problems. An online solutions manual for all even-numbered problems will be made available to instructors.

Mathematical Concepts Of Quantum Mechanics

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Author : Stephen J. Gustafson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-24

Mathematical Concepts Of Quantum Mechanics written by Stephen J. Gustafson 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 2011-09-24 with Mathematics categories.

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory.