A Mathematical Journey Through Differential Equations Of Physics
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A Mathematical Journey Through Differential Equations Of Physics
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Author : Max Lein
language : en
Publisher: World Scientific
Release Date : 2022-09-16
A Mathematical Journey Through Differential Equations Of Physics written by Max Lein and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-16 with Science categories.
Mathematics is the language of physics, and over time physicists have developed their own dialect. The main purpose of this book is to bridge this language barrier, and introduce the readers to the beauty of mathematical physics. It shows how to combine the strengths of both approaches: physicists often arrive at interesting conjectures based on good intuition, which can serve as the starting point of interesting mathematics. Conversely, mathematicians can more easily see commonalities between very different fields (such as quantum mechanics and electromagnetism), and employ more advanced tools.Rather than focusing on a particular topic, the book showcases conceptual and mathematical commonalities across different physical theories. It translates physical problems to concrete mathematical questions, shows how to answer them and explains how to interpret the answers physically. For example, if two Hamiltonians are close, why are their dynamics similar?The book alternates between mathematics- and physics-centric chapters, and includes plenty of concrete examples from physics as well as 76 exercises with solutions. It exploits that readers from either end are familiar with some of the material already. The mathematics-centric chapters provide the necessary background to make physical concepts mathematically precise and establish basic facts. And each physics-centric chapter introduces physical theories in a way that is more friendly to mathematicians.As the book progresses, advanced material is sprinkled in to showcase how mathematics and physics augment one another. Some of these examples are based on recent publications and include material which has not been covered in other textbooks. This is to keep it interesting for the readers.
A Journey Into Partial Differential Equations
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Author : William O. Bray
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 2012
A Journey Into Partial Differential Equations written by William O. Bray and has been published by Jones & Bartlett Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Part of the International Series in Mathematics Ideal for the 1-term course, A Journey into Partial Differential Equations provides a solid introduction to PDEs for the undergraduate math, engineering, or physics student. Discussing underlying physics, concepts and methodologies, the text focuses on the classical trinity of equations: the wave equation, heat/diffusion equation, and Laplace's equation. Bray provides careful treatment of the separation of variables and the Fourier method, motivated by the geometrical notion of symmetries and places emphasis on both the qualitative and quantitative methods, as well as geometrical perspectives. With hundred of exercises and a wealth of figures, A Journey into Partial Differential Equations proves to be the model book for the PDE course.
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.
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.
Mathematical Methods Of Theoretical Physics
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Author : Karl Svozil
language : en
Publisher: World Scientific
Release Date : 2020-02-24
Mathematical Methods Of Theoretical Physics written by Karl Svozil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-24 with Science categories.
'This book could serve either as a good reference to remind students about what they have seen in their completed courses or as a starting point to show what needs more investigation. Svozil (Vienna Univ. of Technology) offers a very thorough text that leaves no mathematical area out, but it is best described as giving a synopsis of each application and how it relates to other areas … The text is organized well and provides a good reference list. Summing Up: Recommended. Upper-division undergraduates and graduate students.'CHOICEThis book contains very explicit proofs and demonstrations through examples for a comprehensive introduction to the mathematical methods of theoretical physics. It also combines and unifies many expositions of this subject, suitable for readers with interest in experimental and applied physics.
Nonlinear Pdes
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Author : Marius Ghergu
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-21
Nonlinear Pdes written by Marius Ghergu 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 2011-10-21 with Mathematics categories.
The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations.
Partial Differential Equations Of Mathematical Physics
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Author : S. L. Sobolev
language : en
Publisher: Courier Corporation
Release Date : 1964-01-01
Partial Differential Equations Of Mathematical Physics written by S. L. Sobolev and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964-01-01 with Science categories.
This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.
The Complex Universe A Journey Through Mathematical Dimensions
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-04-08
The Complex Universe A Journey Through Mathematical Dimensions written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-08 with Mathematics categories.
Embark on an enthralling journey into the realm of complex numbers, where numbers transcend their familiar boundaries and unveil a world of mathematical wonders. Discover the elegance and power of complex numbers as they unlock hidden patterns and reveal intricate relationships that govern our universe. This comprehensive guidebook delves into the fascinating world of complex numbers, providing a thorough exploration of their properties, applications, and the profound impact they have had on various fields of science and engineering. With engaging explanations, illuminating examples, and thought-provoking exercises, this book is an invaluable resource for students, researchers, and professionals seeking to expand their understanding of this captivating mathematical realm. The book begins by introducing the concept of complex numbers, their representation on the complex plane, and their fundamental operations. It then delves into the rich tapestry of complex functions, exploring their unique properties and behavior. Through detailed explanations and illustrative examples, readers will gain a deep understanding of complex integration, differentiation, and the Cauchy-Riemann equations. The book also delves into the applications of complex numbers in diverse fields. Readers will discover how complex numbers are used to model and analyze electrical circuits, fluid flow, and heat transfer. They will also explore the role of complex numbers in quantum mechanics, where they are essential for describing the wave function of particles. Whether you are a student seeking to master complex analysis, a researcher pushing the boundaries of mathematical knowledge, or an engineer seeking to harness the power of complex numbers in practical applications, this book is an indispensable guide to this fascinating mathematical realm. Its comprehensive coverage, engaging narrative, and abundance of exercises make it an invaluable resource for anyone seeking to unlock the secrets of complex numbers. With its captivating explanations, illuminating examples, and thought-provoking exercises, this book is an essential addition to the library of anyone seeking to delve into the enigmatic world of complex numbers. If you like this book, write a review!
A Journey Through Nonlinear Functional Analysis And Its Applications
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date :
A Journey Through Nonlinear Functional Analysis And Its Applications written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In the realm of mathematics, nonlinear functional analysis stands as a beacon of innovation, illuminating the complexities of nonlinear operators and their far-reaching applications. This comprehensive volume, "A Journey Through Nonlinear Functional Analysis and Its Applications," invites readers to embark on an enlightening odyssey into this captivating mathematical landscape. With meticulous explanations, insightful examples, and a captivating narrative, this book unveils the elegance and practical significance of nonlinear functional analysis. Its meticulously crafted chapters guide readers through the fundamental concepts and techniques of nonlinear functional analysis, laying a solid foundation for understanding its diverse applications. Delving into a myriad of fields, this book showcases the transformative power of nonlinear functional analysis in addressing intricate problems in mathematical physics, engineering, economics, finance, and beyond. Readers will discover how nonlinear functional analysis empowers researchers and practitioners to gain deeper insights into complex phenomena, leading to groundbreaking advancements in various disciplines. Written with both clarity and rigor, this book caters to a broad audience, encompassing students, researchers, and practitioners seeking to expand their knowledge and expertise in nonlinear functional analysis. Its comprehensive coverage, engaging writing style, and abundance of illustrative examples make it an invaluable resource for anyone seeking to master this powerful mathematical tool. Throughout this intellectual journey, readers will gain a comprehensive grasp of nonlinear functional analysis and its far-reaching applications, empowering them to tackle intricate problems with renewed confidence and ingenuity. "A Journey Through Nonlinear Functional Analysis and Its Applications" is an essential guide for anyone seeking to delve into the depths of this captivating mathematical field and unlock its transformative potential. If you like this book, write a review!