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First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.
What are the relations between the shape of a system of cities and that of fish school? Which events should happen in a cell in order that it participates to one of the finger of our hands? How to interpret the shape of a sand dune? This collective book written for the non-specialist addresses these questions and more generally, the fundamental issue of the emergence of forms and patterns in physical and living systems. It is a single book gathering the different aspects of morphogenesis and approaches developed in different disciplines on shape and pattern formation. Relying on the seminal works of D’Arcy Thompson, Alan Turing and René Thom, it confronts major examples like plant growth and shape, intra-cellular organization, evolution of living forms or motifs generated by crystals. A book essential to understand universal principles at work in the shapes and patterns surrounding us but also to avoid spurious analogies.
In this large-format book, lavishly illustrated in color throughout, Allan McRobie takes the reader on an alluring exploration of the beautiful curves that shape our world--from our bodies to Salvador Dalí's paintings and the space-time fabric of the universe itself. The book focuses on seven curves--the fold, cusp, swallowtail, and butterfly, plus the hyperbolic, elliptical, and parabolic "umbilics"--and describes the surprising origins of their taxonomy in the catastrophe theory of mathematician René Thom.
This classic book helps students learn the basics in physics by bridging the gap between mathematics and the basic fundamental laws of physics. With supplemental material such as graphs and equations, Mathematical Methods for Physics creates a strong, solid anchor of learning. The text has three parts: Part I focuses on the use of special functions in solving the homogeneous partial differential equations of physics, and emphasizes applications to topics such as electrostatics, wave guides, and resonant cavities, vibrations of membranes, heat flow, potential flow in fluids, plane and spherical waves. Part II deals with the solution of inhomogeneous differential equations with particular emphasis on problems in electromagnetism, Green's functions for Poisson's equation, the wave equation and the diffusion equation, and the solution of integral equations by iteration, eigenfunction expansion and the Fredholm series. Finally, Part II explores complex variable techniques, including evalution of itegrals, dispersion relations, special functions in the complex plane, one-sided Fourier transforms, and Laplace transforms.
Graduate students in both theoretical and experimental physics will find this third edition of Intermediate Quantum Mechanics , refined and updated in 1986, indispensable. The first part of the book deals with the theory of atomic structure, while the second and third parts deal with the relativistic wave equations and introduction to field theory, making Intermediate Quantum Mechanics more complete than any other single-volume work on the subject.
This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.
The topic of this Mosbach Colloquium was meant as a question to begin with. When I started to study differentiation and morphogenesis in Volvox I hoped for a straightforward answer along prepared groove- only to find out that also here things follow Murphy's Law: they were much more complicated than expected! Succour had to be sought. Thus, the idea arose to put this question before a board of experts. Experience would have warned any ex-service man never to utter an idea or else you would be made responsible, and it came as it had to come: I was made impressario of this gremium; I had to assemble the experts. These Proceedings contain their expertise. I cannot even say that I biased it by my picking. In the beginning I aimed at setting different accents by inclination and force of habit. Then, by trial and error, by advice and declination, the programme shaped itself. It eventually gained momentum of which also the size of this volume is indicative. In this volume are printed all the papers presented - with two regret ted exceptions - but not the sometimes lively discussion, which clari fied and pruned here and there. It would just have made the size too unwieldy. Differentiation and morphogenesis start with the expression of genes. The development programme reels off the genome and is regulated by the position of the appropriate genes. Their structure is in the focus of gene biochemistry since the decisive tools have become available.