Geometry

By Sun-Yung Alice Chang

ISBN-10: 303719006X

ISBN-13: 9783037190067

Non-linear elliptic partial differential equations are an incredible instrument within the examine of Riemannian metrics in differential geometry, specifically for difficulties in regards to the conformal switch of metrics in Riemannian geometry. in recent times the function performed through the second one order semi-linear elliptic equations within the research of Gaussian curvature and scalar curvature has been prolonged to a family members of absolutely non-linear elliptic equations linked to different symmetric features of the Ricci tensor. A case of specific curiosity is the second one symmetric functionality of the Ricci tensor in measurement 4 heavily regarding the Pfaffian. In those lectures, ranging from the historical past fabric, the writer reports the matter of prescribing Gaussian curvature on compact surfaces. She then develops the analytic instruments (e.g., better order conformal invariant operators, Sobolev inequalities, blow-up research) which will resolve a completely nonlinear equation in prescribing the Chern-Gauss-Bonnet integrand on compact manifolds of size 4. the fabric is acceptable for graduate scholars and examine mathematicians drawn to geometry, topology, and differential equations. disbursed in the Americas via the yank Mathematical Society.

By Demeter Krupka

ISBN-10: 946239072X

ISBN-13: 9789462390720

ISBN-10: 9462390738

ISBN-13: 9789462390737

The e-book is dedicated to contemporary examine within the international variational conception on soft manifolds. Its major target is an extension of the classical variational calculus on Euclidean areas to (topologically nontrivial) finite-dimensional gentle manifolds; to this function the equipment of worldwide research of differential kinds are used. Emphasis is put on the principles of the idea of variational functionals on fibered manifolds - proper geometric constructions for variational ideas in geometry, actual box idea and higher-order fibered mechanics. The publication chapters contain: - foundations of jet bundles and research of differential varieties and vector fields on jet bundles, - the speculation of higher-order critical variational functionals for sections of a fibred house, the (global) first variational formulation in infinitesimal and indispensable varieties- extremal stipulations and the dialogue of Noether symmetries and generalizations,- the inverse difficulties of the calculus of adaptations of Helmholtz sort- variational series thought and its results for the worldwide inverse challenge (cohomology conditions)- examples of variational functionals of mathematical physics. whole formulations and proofs of all simple assertions are given, in response to theorems of worldwide research defined within the Appendix.

By Helmut Pottmann, Johannes Wallner

ISBN-10: 3642040179

ISBN-13: 9783642040177

From the reports: " a special and engaging combination, that is proven to be invaluable for various purposes, together with robotics, geometrical optics, desktop animation, and geometric layout. The contents of the e-book are visualized by means of a wealth of conscientiously selected illustrations, making the booklet a shear excitement to learn, or perhaps to only browse in." Mathematical experiences

By Ilka Agricola, Thomas Friedrich

ISBN-10: 3658067306

ISBN-13: 9783658067304

ISBN-10: 3658067314

ISBN-13: 9783658067311

Das vorliegende Lehrbuch führt in alle unterrichtsrelevanten Themen der Elementargeometrie ein. Es eignet sich als Begleitbuch zur gleichnamigen Vorlesung für Studierende des Lehramts Mathematik sowohl in den Bachelor- als auch in den Staatsexamensstudiengängen. Die beiden letzten Kapitel eignen sich für vertiefende Lehrveranstaltungen und bieten viele mögliche Themen für Seminar- und Studienarbeiten. Die four. Auflage wurde sorgfältig überarbeitet und erweitert. Manche Themenkomplexe sind nun ausführlicher dargestellt worden. Einige Abbildungen geometrischer Modelle wurden ergänzt und die Anzahl der Übungsaufgaben wurde weiter erhöht. Am Ende des Buches findet der Leser Lösungen ausgewählter Aufgaben zu allen Kapiteln; das Buch ist so sehr intestine zur Prüfungsvorbereitung geeignet. Die Autoren bieten darüber hinaus einen besonderen provider an: Jeder Studierende, der beim Lösen der Übungsaufgaben auf Schwierigkeiten stößt, kann sich according to email direkt an die Autoren wenden.

By Benno Artmann

ISBN-10: 1461214122

ISBN-13: 9781461214120

ISBN-10: 1461271347

ISBN-13: 9781461271345

This publication is for all enthusiasts ofmathematics. it's an try and less than­ stand the character of arithmetic from the viewpoint of its most vital early resource. no matter if the cloth lined by way of Euclid will be thought of ele­ mentary for the main half, the best way he offers it has set the normal for greater than thousand years. realizing Euclid's components might be ofthe similar significance for a mathematician this present day as figuring out Greek structure is for an architect. truly, no con­ transitority architect will build a Doric temple, not to mention manage a development website within the method the ancients did. yet for the learning ofan architect's aesthetic judgment, an information ofthe Greek her­ itage is vital. I believe Peter Hilton while he says that real arithmetic constitutesone ofthe most interesting expressions ofthe human spirit, and that i may perhaps upload that the following as in such a lot of different situations, we've discovered that language ofexpression from the Greeks. whereas providing geometry and mathematics Euclid teaches us es­ sential beneficial properties of arithmetic in a way more normal feel. He monitors the axiomatic origin of a mathematical thought and its wakeful improvement in the direction of the answer of a particular challenge. We see how abstraction works and enforces the strictly deductive presentation ofa idea. We research what inventive definitions are and v VI ----=P:. . :re:. ::::fa=ce how a conceptual grab ends up in toe class ofthe suitable ob­ jects.

By Otto Schreier, Emanuel Sperner

By Dawn Griffiths, Lindsey Fallow

Having hassle with geometry? Do Pi, The Pythagorean Theorem, and perspective calculations simply make your head spin? chill out. With Head First second Geometry, you'll grasp every thing from triangles, quads and polygons to the time-saving secrets and techniques of comparable and congruent angles -- and it'll be fast, painless, and fun.

via pleasing tales and useful examples from the realm round you, this publication takes you past dull difficulties. You'll really use what you learn how to make real-life judgements, like utilizing angles and parallel traces to crack a mysterious CSI case. positioned geometry to give you the results you want, and nail your type checks alongside the way.

we predict a while is just too beneficial to waste suffering from new recommendations. utilizing the newest learn in cognitive technological know-how and studying concept to craft a multi-sensory studying adventure, Head First second Geometry makes use of a visually-rich layout designed for how your mind works, now not a text-heavy process that places you to sleep.

By Gurevich G.B.

By Beverly Nance

By Elmer G. Rees

ISBN-10: 354012053X

ISBN-13: 9783540120537

Lately, geometry has performed a lesser position in undergraduate classes than it has ever performed. however, it nonetheless performs a number one position in arithmetic at a better point. Its principal position within the historical past of arithmetic hasn't ever been disputed. it's important, as a result, to introduce a few geometry into college syllabuses. There are numerous methods of doing this, it may be included into current classes which are essentially dedicated to different subject matters, it may be taught at a primary yr point or it may be taught in better point classes dedicated to differential geometry or to extra classical issues. those notes are meant to fill a slightly noticeable hole within the literature. It treats the classical subject matters of Euclidean, projective and hyperbolic geometry yet makes use of the fabric quite often taught to undergraduates: linear algebra, crew concept, metric areas and intricate research. The notes are in response to a path whose target was once fold, to start with, to introduce the scholars to a couple geometry and secondly to deepen their realizing of subject matters that they've already met. what's required from the sooner fabric is a familiarity with the most principles, particular issues which are used tend to be redone.