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Author: Don Koks
Publisher: Springer Science & Business Media
ISBN: 0387309438
Category : Science
Languages : en
Pages : 549
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Book Description
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.
Author: Don Koks
Publisher: Springer Science & Business Media
ISBN: 0387309438
Category : Science
Languages : en
Pages : 549
Get Book Here
Book Description
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.
Author: Alan F. Beardon
Publisher: Cambridge University Press
ISBN: 131661056X
Category : Mathematics
Languages : en
Pages : 129
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Book Description
Provides readers with experience of working on difficult unsolved problems. No deep mathematical background is required.
Author: Ronald W. Shonkwiler
Publisher: Springer Science & Business Media
ISBN: 0387878378
Category : Mathematics
Languages : en
Pages : 249
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Book Description
Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems. Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics.
Author: Robert Osserman
Publisher: Anchor
ISBN: 0307790584
Category : Science
Languages : en
Pages : 225
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Book Description
In the bestselling literary tradition of Lewis Thomas's Lives of a Cell and James Watson's The Double Helix, Poetry of the Universe is a delightful and compelling narrative charting the evolution of mathematical ideas that have helped to illuminate the nature of the observable universe. In a richly anecdotal fashion, the book explores teh leaps of imagination and vision in mathematics that have helped pioneer our understanding of the world around us.
Author: Don Koks
Publisher: Springer
ISBN: 3030024296
Category : Science
Languages : en
Pages : 560
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Book Description
Statistical mechanics: the bane of many a physics student, and traditionally viewed as a long parade of ensembles, partition functions, and partial derivatives. But the subject needn't be arcane. When pared back to its underlying concepts and built from the ground up, statistical mechanics takes on a charm of its own, and sheds light on all manner of physical phenomena. This book presents a straightforward introduction to the key concepts in statistical mechanics, following the popular style of the author's highly successful textbook "Explorations in Mathematical Physics". Offering a clear, conceptual approach to the subject matter, the book presents a treatment that is mathematically complete, while remaining very accessible to undergraduates. It commences by asking: why does an ink drop spread out in a bathtub of water? This showcases the importance of counting configurations, which leads naturally to ideas of microstates, energy, entropy, thermodynamics, and physical chemistry. With this foundation, the Boltzmann distribution writes itself in its fullest form, and this opens the door to the Maxwell distribution and related areas of thermal conductivity and viscosity. Quantum ideas then appear: bosons via Einstein's and Debye's theories of heat capacity, and fermions via electrical conduction and low-temperature heat capacity of metals. The text ends with a detailed derivation of blackbody radiation, and uses this to discuss the greenhouse effect, lasers, and cosmology. Suitable for use with core undergraduate courses in statistical mechanics and thermodynamics, this book concentrates on using solid mathematics, while avoiding cumbersome notation. All the necessary mathematical steps are included in the body of the text and in the worked examples. Reviews of Explorations in Mathematical Physics by Don Koks, 2006 "With enjoyable and sometimes surprising excursions along the way, the journey provides a fresh look at many familiar topics, as it takes us from basic linear mathematics to general relativity... look forward to having your geometric intuition nourished and expanded by the author's intelligent commentaries." (Eugen Merzbacher, University of North Carolina) "... an interesting supplement to standard texts for teaching mathematical methods in physics, as it will add alternative views that could serve as additional material." (S. Marcelja, Australian Journal of Physics) "... a tour through the main ideas forming the language of modern mathematical physics ...it is a difficult task for the author to decide what is a good balance between the topics and their presentation, but in this case it has been achieved. ...for those physicists who would like to be exposed to clear motivation and careful explanation of the basics of the present-day apparatus of mathematical physics." (Ivailo Mladenov, Mathematical Reviews).
Author: Helena Engelina Nusse
Publisher:
ISBN: 9789789780389
Category : Chaotic behavior in systems
Languages : en
Pages : 484
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Book Description
Author: Alexander Altland
Publisher: Cambridge University Press
ISBN: 1108651151
Category : Science
Languages : en
Pages : 723
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Book Description
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.
Author: Nader Engheta
Publisher: John Wiley & Sons
ISBN: 0471784184
Category : Technology & Engineering
Languages : en
Pages : 438
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Book Description
Leading experts explore the exotic properties and exciting applications of electromagnetic metamaterials Metamaterials: Physics and Engineering Explorations gives readers a clearly written, richly illustrated introduction to the most recent research developments in the area of electromagnetic metamaterials. It explores the fundamental physics, the designs, and the engineering aspects, and points to a myriad of exciting potential applications. The editors, acknowledged leaders in the field of metamaterials, have invited a group of leading researchers to present both their own findings and the full array of state-of-the-art applications for antennas, waveguides, devices, and components. Following a brief overview of the history of artificial materials, the publication divides its coverage into two major classes of metamaterials. The first half of the publication examines effective media with single (SNG) and double negative (DNG) properties; the second half examines electromagnetic band gap (EBG) structures. The book further divides each of these classes into their three-dimensional (3D volumetric) and two-dimensional (2D planar or surface) realizations. Examples of each type of metamaterial are presented, and their known and anticipated properties are reviewed. Collectively, Metamaterials: Physics and Engineering Explorations presents a review of recent research advances associated with a highly diverse set of electromagnetic metamaterials. Its multifaceted approach offers readers a combination of theoretical, numerical, and experimental perspectives for a better understanding of their behaviors and their potentialapplications in components, devices, and systems. Extensive reference lists provide opportunities to explore individual topics and classes of metamaterials in greater depth. With full-color illustrations throughout to clarify concepts and help visualize actual results, this book provides a dynamic, user-friendly resource for students, engineers, physicists, and other researchers in the areas of electromagnetic materials, microwaves, millimeter waves, and optics. It equips newcomers with a basic understanding of metamaterials and their potential applications. Advanced researchers will benefit from thought-provoking perspectives that will deepen their knowledge and lead them to new areas of investigation.
Author: John Stewart
Publisher: Cambridge University Press
ISBN: 9780521449465
Category : Science
Languages : en
Pages : 244
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Book Description
A self-contained introduction to advanced general relativity.
Author: Ian Stewart
Publisher: OUP Oxford
ISBN: 0191624802
Category : Games & Activities
Languages : en
Pages : 320
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Book Description
From the mathematics of mazes, to cones with a twist, and the amazing sphericon - and how to make one - Ian Stewart is back with more mathematical stories and puzzles that are as quirky as they are fascinating, and each from the cutting edge of the world of mathematics. We find out about the mathematics of time travel, explore the shape of teardrops (which are not tear-drop shaped, but something much, much more strange!), dance with dodecahedra, and play the game of Hex, amongst many more strange and delightful mathematical diversions.
