Category: Mathematical Physics

By Rosario N. Mantegna

Statistical physics innovations akin to stochastic dynamics, brief- and long-range correlations, self-similarity and scaling, enable an figuring out of the worldwide habit of financial platforms with out first having to see a close microscopic description of the approach. This pioneering textual content explores using those thoughts within the description of monetary platforms, the dynamic new distinctiveness of econophysics. The authors illustrate the scaling thoughts utilized in likelihood conception, serious phenomena, and fully-developed turbulent fluids and observe them to monetary time sequence. additionally they current a brand new stochastic version that monitors numerous of the statistical homes saw in empirical information. Physicists will locate the applying of statistical physics innovations to financial platforms interesting. Economists and different monetary execs will enjoy the book's empirical research equipment and well-formulated theoretical instruments that may let them describe platforms composed of an incredible variety of interacting subsystems.

By Walter William Rouse Ball

For hundreds of years, Cambridge college has attracted the various world's maximum mathematicians. This 1889 ebook offers a compelling account of ways arithmetic built at Cambridge from the center a while to the overdue 19th century, from the point of view of a number one pupil dependent at Trinity university who used to be heavily inquisitive about instructing the topic. The achievements of striking participants together with Newton and his university are set within the context of the historical past of the college, its occasionally uneasy dating with town neighborhood, the varsity procedure, and the foundation and development of the mathematical tripos.

By Jenny Olive

I'm a arithmetic instructor, on the secondary, group university, and school (undergrad and graduate) point. This booklet doesn't handle the elemental wishes of the suffering scholar, particularly: what's arithmetic for? extra, the publication is verbose in order that even the winning scholar gets slowed down within the sheer value of the e-book.

By Robert T. Glassey

This truly written, self-contained quantity reviews the fundamental equations of kinetic conception in all of area. It comprises updated, cutting-edge remedies of initial-value difficulties for the most important kinetic equations, together with the Boltzmann equation (from rarefied gasoline dynamics) and the Vlasov-Poisson/Vlasov-Maxwell platforms (from plasma physics). this is often the one present booklet to regard Boltzmann-type difficulties and Vlasov-type difficulties jointly. even though those equations describe very varied phenomena, they proportion an identical streaming time period. the writer proves that suggestions ranging from a given configuration at an preliminary time exist for all destiny occasions by means of implementing acceptable hypotheses at the preliminary values in numerous very important circumstances. He emphasizes these questions mathematician could ask first: Is there an answer to this challenge? Is it distinctive? Can it's numerically approximated?

By Paul J. Nahin

What does quilting need to do with electrical circuit idea? the answer's only one of the attention-grabbing ways in which best-selling well known math author Paul Nahin illustrates the deep interaction of math and physics on the planet round us in his most modern publication of tough mathematical puzzles, Mrs. Perkins's electrical duvet. along with his trademark blend of interesting mathematical difficulties and the historic anecdotes surrounding them, Nahin invitations readers on a thrilling and informative exploration of a few of the various methods math and physics mix to create anything greatly extra strong, priceless, and fascinating than both is on its own. In a chain of short and mostly self-contained chapters, Nahin discusses a variety of themes during which math and physics are together established and together illuminating, from Newtonian gravity and Newton's legislation of mechanics to ballistics, air drag, and electrical energy. The mathematical topics diversity from algebra, trigonometry, geometry, and calculus to differential equations, Fourier sequence, and theoretical and Monte Carlo chance. every one bankruptcy comprises problems--some 3 dozen in all--that problem readers to attempt their hand at utilising what they've got realized. simply as in his different books of mathematical puzzles, Nahin discusses the historic history of every challenge, offers many examples, contains MATLAB codes, and offers whole and particular suggestions on the finish. Mrs. Perkins's electrical duvet will attract scholars drawn to new math and physics functions, lecturers searching for strange examples to take advantage of in class--and a person who enjoys renowned math books.

By Ignazio Licata

By George W. Bluman

This ebook offers a complete remedy of symmetry equipment and dimensional research. The authors talk about facets of Lie teams of aspect adjustments, touch symmetries, and better order symmetries which are crucial for fixing differential equations. Emphasis is given to an algorithmic, computational method of discovering integrating components and primary integrals. various examples together with usual differential equations coming up in utilized arithmetic are used for representation and workout units are incorporated in the course of the textual content. This e-book is designed for complicated undergraduate or starting graduate scholars of arithmetic and physics, in addition to researchers in arithmetic, physics, and engineering.

By Richard Herrmann

The publication offers a concise advent to the fundamental equipment and methods in fractional calculus and allows the reader to meet up with the cutting-edge during this box in addition to to take part and give a contribution within the improvement of this intriguing examine zone. The contents are dedicated to the appliance of fractional calculus to actual difficulties. The fractional inspiration is utilized to topics in classical mechanics, workforce idea, quantum mechanics, nuclear physics, hadron spectroscopy and quantum box concept and it'll shock the reader with new fascinating insights. This new, prolonged variation now additionally covers extra chapters approximately snapshot processing, folded potentials in cluster physics, infrared spectroscopy and native elements of fractional calculus. a brand new function is workouts with elaborated suggestions, which considerably helps a deeper realizing of basic elements of the idea. consequently, this e-book also needs to be necessary as a aiding medium for academics and classes dedicated to this topic

By Werner Ruhl

By Stephen Bruce Sontz

This introductory textual content is the 1st publication approximately quantum imperative bundles and their quantum connections that are typical generalizations to non-commutative geometry of critical bundles and their connections in differential geometry. To make for a extra self-contained e-book there's additionally a lot history fabric on Hopf algebras, (covariant) differential calculi, braid teams and appropriate conjugation operations. The procedure is sluggish paced and intuitive on the way to supply researchers and scholars in either arithmetic and physics prepared entry to the material.