By Jacques Lafontaine
This e-book is an advent to differential manifolds. It offers strong preliminaries for extra complicated subject matters: Riemannian manifolds, differential topology, Lie concept. It presupposes little historical past: the reader is barely anticipated to grasp uncomplicated differential calculus, and a bit point-set topology. The e-book covers the most themes of differential geometry: manifolds, tangent area, vector fields, differential kinds, Lie teams, and some extra subtle issues reminiscent of de Rham cohomology, measure conception and the Gauss-Bonnet theorem for surfaces.
Its ambition is to offer sturdy foundations. specifically, the advent of “abstract” notions equivalent to manifolds or differential types is prompted through questions and examples from arithmetic or theoretical physics. greater than a hundred and fifty routines, a few of them effortless and classical, a few others extra refined, may help the newbie in addition to the extra specialist reader. ideas are supplied for many of them.
The booklet may be of curiosity to numerous readers: undergraduate and graduate scholars for a primary touch to differential manifolds, mathematicians from different fields and physicists who desire to collect a few feeling approximately this pretty theory.
The unique French textual content creation aux variétés différentielles has been a best-seller in its class in France for plenty of years.
Jacques Lafontaine was once successively assistant Professor at Paris Diderot college and Professor on the college of Montpellier, the place he's shortly emeritus. His major learn pursuits are Riemannian and pseudo-Riemannian geometry, together with a few features of mathematical relativity. along with his own study articles, he used to be desirous about a number of textbooks and examine monographs.
Read or Download An Introduction to Differential Manifolds PDF
Similar geometry & topology books
What precisely is the Golden Ratio? How used to be it chanced on? the place is it discovered? those questions and extra are completely defined during this attractive travel of 1 of arithmetic' best phenomena. The authors trace the looks of the Golden Ratio all through heritage, show quite a few inventive concepts used to build it, and illustrate the numerous unbelievable geometric figures during which the Golden Ratio is embedded.
Langer als ursprunglich beabsichtigt warfare, hat sich die fortress setzung des Werkes verzogert, . . von dessen zweitem Bande nunmehr ein erster Theil der Oeffentlichkeit ubergeben wird. Mannigfache eigene Untersuchungen und eine umfangreiche amtliche Thatigkeit nahmen mich lange Zeit zu sehr in Anspruch. Ueberdies warfare mir die Freude an der Arbeit wesentlich beeintrachtigt, theils durch mehrfach ungiinstige U rtheile u ber die paintings und Weise, wie ich im ersten Bande iiber den ursprunglichen Inhalt von Cle bsch' s Vor lesungen durch Bearbeitung neuerer Untersuchungen hinausgegangen struggle, theils durch das Bewusstsein, in der That nicht immer das vor gesteckte Ziel erreicht zu haben.
I used to be instructing in united states for twenty years in university method and 31 years in numerous state. My enormous event aid me to provide scholar very good wisdom. This e-book contain extremely important subject to achieve success scholar in any schools. This ebook contain assessment of arithmetic:whole numbers, decimals, fractions and combined numbers, rational numbers, introductions of equations, polynomial, geometry, note difficulties.
This ebook specializes in the unifying strength of the geometrical language in bringing jointly suggestions from many alternative parts of physics, starting from classical physics to the theories describing the 4 primary interactions of Nature — gravitational, electromagnetic, powerful nuclear, and vulnerable nuclear.
- Algebraic Varieties (London Mathematical Society Lecture Note Series)
- Real Algebraic Geometry: 66 (UNITEXT)
- General Topology (Dover Books on Mathematics)
- Random Fields and Geometry (Springer Monographs in Mathematics)
- General Cohomology Theory and K-Theory (London Mathematical Society Lecture Note Series)
Extra info for An Introduction to Differential Manifolds
An Introduction to Differential Manifolds by Jacques Lafontaine