By Michael K. Murray, John W. Rice (auth.)
By Michael K. Murray, John W. Rice (auth.)
By Shui-Nee Chow
This publication is especially involved in the bifurcation concept of ODEs. Chapters 1 and a couple of of the ebook introduce systematic equipment of simplifying equations: heart manifold idea and basic shape concept, during which one may perhaps lessen the measurement of equations and alter types of equations to be so simple as attainable. Chapters 3-5 of the publication examine in substantial element the bifurcation of these one or dimensional equations with one, or a number of parameters.
By A.N. Parshin (editor), I.R. Shafarevich (editor), I. Rivin, V.S. Kulikov, P.F. Kurchanov, V.V. Shokurov
This two-part EMS quantity presents a succinct precis of complicated algebraic geometry, coupled with a lucid creation to the hot paintings at the interactions among the classical quarter of the geometry of advanced algebraic curves and their Jacobian kinds. a superb better half to the older classics at the topic.
By Vladimir E. Nazaikinskii, Anton Yu. Savin, Bert-Wolfgang Schulze, Boris Yu. Sternin
The research and topology of elliptic operators on manifolds with singularities are even more complex than within the tender case and require thoroughly new mathematical notions and theories. whereas there has lately been a lot growth within the box, lots of those effects have remained scattered in journals and preprints. ranging from an user-friendly point and completing with the newest effects, this booklet supplies a scientific exposition of either analytical and topological features of elliptic idea on manifolds with singularities. The presentation contains a evaluation of the most thoughts of the idea of elliptic equations, bargains a comparative research of varied methods to differential equations on manifolds with singularities, and devotes significant cognizance to purposes of the idea. those comprise Sobolev difficulties, theorems of Atiyah-Bott-Lefschetz style, and proofs of index formulation for elliptic operators and difficulties on manifolds with singularities, together with the authors' new technique to the index challenge for manifolds with nonisolated singularities. A thesaurus, a number of illustrations, and lots of examples aid readers grasp the topic. transparent exposition, updated insurance, and accessibility-even on the complex undergraduate level-lay the basis for carrying on with reviews and extra advances within the box.
By Grove K., Madsen I.H., Pedersen E.K. (eds.)
By David R. Morrison, Janos Kolla Summer Research Institute on Algebraic Geometry
By R. Miron, Mihai Anastasiei
Differential-geometric equipment are gaining expanding value within the figuring out of a variety of primary ordinary phenomena. quite often, the place to begin for such experiences is a variational challenge formulated for a handy Lagrangian. From a proper viewpoint, a Lagrangian is a delicate genuine functionality outlined at the overall area of the tangent package to a manifold fulfilling a few regularity stipulations. the most objective of this ebook is to offer: (a) an in depth dialogue of the geometry of the full area of a vector package; (b) a close exposition of Lagrange geometry; and (c) an outline of crucial functions. New equipment are defined for development geometrical types for functions.
a number of the chapters think about subject matters comparable to fibre and vector bundles, the Einstein equations, generalized Einstein--Yang--Mills equations, the geometry of the whole house of a tangent package deal, Finsler and Lagrange areas, relativistic geometrical optics, and the geometry of time-dependent Lagrangians. necessities for utilizing the publication are a superb beginning typically manifold idea and a basic heritage in geometrical versions in physics.
For mathematical physicists and utilized mathematicians attracted to the idea and purposes of differential-geometric tools.
By Victor A. Toponogov (auth.), Vladimir Y. Rovenski (eds.)
The learn of curves and surfaces varieties an enormous a part of classical differential geometry. Differential Geometry of Curves and Surfaces: A Concise Guide provides conventional fabric during this box in addition to very important rules of Riemannian geometry. The reader is brought to curves, then to surfaces, and at last to extra complicated subject matters. usual theoretical fabric is mixed with more challenging theorems and intricate difficulties, whereas keeping a transparent contrast among the 2 levels.
Key issues and features:
* Covers critical thoughts together with curves, surfaces, geodesics, and intrinsic geometry
* substantive fabric at the Aleksandrov worldwide perspective comparability theorem, which the writer generalized for Riemannian manifolds (a end result referred to now because the celebrated Toponogov comparability Theorem, one of many cornerstones of contemporary Riemannian geometry)
* comprises many nontrivial and unique difficulties, a few with tricks and solutions
This rigorous exposition, with well-motivated subject matters, is perfect for complicated undergraduate and first-year graduate scholars looking to input the attention-grabbing international of geometry.
By Vagn Lundsgaard Hansen
1. Geometric types in Nature. 1. Spirals and the glorious Snail. 2. The Helix and the Twining Vine. three. The Geometry of cleaning soap movies. four. The Geometry of Tiled Surfaces. five. The ordinary Polyhedra
2. The Topology of Surfaces. 1. a few universal Surfaces. 2. The Projective airplane and the Klein Bottle. three. what's a Closed floor? four. Orientable and Non-Orientable Surfaces. five. hooked up Sum of Closed Surfaces. 6. class of Closed Surfaces. 7. Higher-Dimensional Manifolds and Poincare's Conjecture
three. The Topology of Catastrophes. 1. The starting place of disaster concept. 2. Singularities: Mappings of the airplane into the airplane. three. The Fold disaster. four. The Cusp disaster. five. Thom's Theorem for platforms with regulate Variables and One country Variable. 6. a few functions of the Cusp disaster. 7. the maths at the back of the versions of disaster conception. eight. The Seven ordinary Catastrophes in Space-Time. nine. a few normal feedback bearing on Applications.
four. Geometry and the actual international. 1. On arithmetic and Its Greek Legacy. 2. Greek Astronomy and the Ptolemaic procedure. three. The Copernican global, Tycho Brahe and Kepler. four. The leap forward of recent normal technology. five. Newton and Gravitation
five. Geometry and smooth Physics. 1. Maxwell and the Electromagnetic idea. 2. Einstein's thought of Relativity. three. Minkowski Space-Time and the distinct idea of Relativity. four. Curvature and Gravitation: the final conception of Relativity. five. The Physics of effortless debris. 6. Fiber Bundles and Parallel Displacement in Fiber Bundles. 7. Gauge Theories and String Theories.
By Robert W. Vallin
A systematic and built-in method of Cantor units and their functions to varied branches of mathematics
The components of Cantor units: With purposes features an intensive creation to Cantor units and applies those units as a bridge among genuine research, chance, topology, and algebra.
The writer fills a niche within the present literature through supplying an introductory and built-in standpoint, thereby getting ready readers for additional research and construction a deeper knowing of study, topology, set thought, quantity conception, and algebra.
The parts of Cantor units provides assurance of:
An excellent textual content for classes in genuine research, topology, algebra, and set conception for undergraduate and graduate-level classes inside of arithmetic, machine technology, engineering, and physics departments, The parts of Cantor units is additionally acceptable as an invaluable reference for researchers and secondary arithmetic schooling majors.