Geometry And Topology

Geometric and Trigonometric Optics by Eustace L. Dereniak, Teresa D. Dereniak

By Eustace L. Dereniak, Teresa D. Dereniak

This new and updated e-book covers the trendy geometrical facets of optics, that's the elemental point of realizing the expertise. starting with how mild is generated and the way quick it travels, the ebook discusses how fabrics have interaction with gentle, how quite a few fabrics have an effect on the rate of sunshine, and the ramifications of swap within the pace of sunshine. the idea that of the index of refraction, and the way it really is used with Snell's legislation to supply picture forming platforms, is built. a great textbook for complicated undergraduate point classes in geometrical optics, this e-book also will curiosity these desirous to examine the innovations and conception of geometrical optics. each one bankruptcy includes labored examples, and there are workouts to augment the reader's knowing of fabric.

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Prospects in Complex Geometry: Proceedings of the 25th by Akira Fujiki (auth.), Junjiro Noguchi, Takeo Ohsawa (eds.)

By Akira Fujiki (auth.), Junjiro Noguchi, Takeo Ohsawa (eds.)

In the Teichmüller idea of Riemann surfaces, along with the classical conception of quasi-conformal mappings, vari- ous methods from differential geometry and algebraic geometry have merged in recent times. therefore the relevant topic of "Complex constitution" used to be a well timed selection for the joint conferences in Katata and Kyoto in 1989. The invited contributors exchanged rules on diversified techniques to similar subject matters in complicated geometry and mapped out the customers for the following couple of years of research.

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L.S. Pontryagin: Topological Groups by R. V. Gamkrelidze

By R. V. Gamkrelidze

Delivering the insights of L.S. Pontryagin, one of many most popular thinkers in sleek arithmetic, the second one quantity during this four-volume set examines the character and strategies that make up topological teams. Already hailed because the prime paintings during this topic for its abundance of examples and its thorough reasons, the textual content is prepared in order that readers can stick with the cloth both sequentially or schematically. Stand-alone chapters hide such themes as topological department jewelry, linear representations of compact topological teams, and the idea that of a lie staff.

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Géométrie. Classe de Mathématiques (Programmes de 1945) by Lebossé C., Hémery C.

By Lebossé C., Hémery C.

Réimpression par les éditions Jacques Gabay d’un livre initialement publié par Fernand Nathan en 1961. Conforme au programme du 27 juin 1945.

Table des matières :

Première partie. — Éléments orientés

Leçon 1. — Vecteurs et coordonnées
    Vecteurs
    Sommes vectorielles
    Projections d’un vecteur
    Coordonnées

Leçon 2. — Angles orientés dans le plan
    Angles orientés dans le plan
    Angle de deux droites dans le plan
    Angles inscrits

Leçon three. — Éléments orientés dans l’espace. — Produit scalaire. — kinfolk métriques dans le triangle

Leçon four. — Trièdres
    Trièdres
    Relations entre les faces d’un trièdre
    Trièdres supplémentaires
    Cas d’égalité des trièdres

Deuxième partie. — Transformations

Leçon five. — variations. — Déplacements plans
    Transformations ponctuelles
    Déplacements plans
    Translation plane
    Rotation plane

Leçon 6. — Symétrie-droite dans le plan. — functions des déplacements et symétries

Leçon 7. — Déplacements dans l’espace
    Déplacements dans l’espace
    Translation dans l’espace
    Rotation dans l’espace

Leçon eight. — Symétries dans l’espace. — Comparaison. — Éléments de symétrie d’une figure

Leçon nine. — Homothétie
    Homothétie
    Applications de l’homothétie

Leçon 10. — Similitude dans le plan et dans l’espace

Leçon eleven. — department et faisceau harmoniques
    Division harmonique
    Faisceau harmonique
    Polaire d’un element par rapport à deux droites

Leçon 12. — Puissance par rapport à un cercle et à une sphère

Leçon thirteen. — Cercles orthogonaux. — Faisceaux de cercles. — Sphères orthogonales

Leçon 14. — Polarité par rapport à un cercle et à une sphère

Leçon 15. — Inversion dans le plan et dans l’espace

Leçon sixteen. — functions. — Projection stéréographique

Troisième partie. — Coniques

Introduction

Leçon 17. — Ellipse. — Tangentes à l’ellipse

Leçon 18. — Équation de l’ellipse. — Ellipse projection d’un cercle

Leçon 19. — Hyperbole. — Tangentes à l’hyperbole

Leçon 20. — Équation de l’hyperbole. — Propriétés kin aux asymptotes
    Équation de l’hyperbole
    Propriétés relations aux asymptotes
    Hyperbole équilatère

Leçon 21. — Parabole. — Tangentes à los angeles parabole. — Équation de los angeles parabole

Leçon 22. — Foyers et directrices

Leçon 23. — Propriétés communes
    Lieux géométriques
    Propriétés des tangentes
    Propriétés des normales

Leçon 24. — Sections planes d’un cône ou cylindre de révolution

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Elementary Geometry of Algebraic Curves: An Undergraduate by Jamal T. Manassah

By Jamal T. Manassah

This is an creation to airplane algebraic curves from a geometrical standpoint, designed as a primary textual content for undergraduates in arithmetic, or for postgraduate and learn staff within the engineering and actual sciences. The publication is definitely illustrated and includes a number of hundred labored examples and workouts. From the well-known traces and conics of trouble-free geometry the reader proceeds to normal curves within the genuine affine aircraft, with tours to extra common fields to demonstrate purposes, resembling quantity concept. via including issues at infinity the affine airplane is prolonged to the projective airplane, yielding a normal atmosphere for curves and offering a flood of illumination into the underlying geometry. A minimum volume of algebra results in the well-known theorem of Bezout, whereas the tips of linear structures are used to debate the classical workforce constitution at the cubic.

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Complexity Explained by Peter Erdi

By Peter Erdi

This ebook explains why complicated platforms learn is critical in figuring out the constitution, functionality and dynamics of advanced common and social phenomena. It illuminates how advanced collective habit emerges from the elements of a procedure, because of the interplay among the procedure and its surroundings. you'll examine the elemental thoughts and techniques of advanced procedure learn. it truly is proven that very varied complicated phenomena of nature and society might be analyzed and understood through nonlinear dynamics when you consider that many structures of very diverse fields, akin to physics, chemistry, biology, economics, psychology and sociology and so forth. have comparable structure. "Complexity defined" isn't really hugely technical and mathematical, yet teaches and makes use of the elemental mathematical notions of dynamical method conception making the ebook invaluable for college kids of technological know-how majors and graduate classes, however it will be readable for a extra basic viewers; really for these, who ask: What complicated structures rather are?

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Geometry and Spectra of Compact Riemann Surfaces by Peter Buser (auth.)

By Peter Buser (auth.)

This vintage monograph is a self-contained advent to the geometry of Riemann surfaces of continuous curvature –1 and their size and eigenvalue spectra. It makes a speciality of topics: the geometric conception of compact Riemann surfaces of genus more than one, and the connection of the Laplace operator with the geometry of such surfaces. the 1st a part of the ebook is written in textbook shape on the graduate point, with basically minimum requirements in both differential geometry or complicated Riemann floor conception. the second one a part of the e-book is a self-contained creation to the spectrum of the Laplacian in keeping with the warmth equation. Later chapters take care of fresh advancements on isospectrality, Sunada’s building, a simplified facts of Wolpert’s theorem, and an estimate of the variety of pairwise isospectral non-isometric examples which relies in basic terms on genus. Researchers and graduate scholars drawn to compact Riemann surfaces will locate this ebook an invaluable reference. Anyone accustomed to the author's hands-on method of Riemann surfaces could be gratified by way of either the breadth and the intensity of the themes thought of the following. The exposition can also be super transparent and thorough. an individual no longer acquainted with the author's technique is in for a true deal with. — Mathematical ReviewsThis is a thick and leisurely e-book in an effort to pay off repeated learn with many friendly hours – either for the newbie and the specialist. it really is thankfully roughly self-contained, which makes it effortless to learn, and it leads one from crucial arithmetic to the “state of the artwork” within the idea of the Laplace–Beltrami operator on compact Riemann surfaces. even though it isn't encyclopedic, it's so wealthy in details and concepts … the reader should be thankful for what has been incorporated during this very pleasant booklet. —Bulletin of the AMS The publication is especially good written and relatively available; there's a very good bibliography on the finish. —Zentralblatt MATH

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