Download E-books Geometric Measure Theory: An Introduction (2010 re-issue) PDF

By Xiaoping Yang

Because the booklet of the seminal paintings of H. Federer which provides a slightly whole and entire dialogue at the topic, the geometric degree idea has built within the final 3 many years into a fair extra cohesive physique of simple wisdom with an abundant constitution of its personal, setting up powerful ties with many different parts of arithmetic and made a number of new notable functions. the current publication is meant for the researchers in different fields of arithmetic in addition to graduate scholars for a fast evaluate as regards to the geometric degree thought emphasizing on numerous uncomplicated rules, concepts and their functions in difficulties coming up within the calculus of adaptations, geometrical research and nonlinear partial differential equations. This graduate-level remedy of Geometric degree concept illustrates with concrete examples and emphasizes simple rules and methods with their purposes to the calculus of adaptations, geometrical research, and nonlinear PDEs. The booklet, as well as an entire index and bibliography, comprise 8 major chapters. New paperback re-issue.

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Download E-books Comment résoudre les problèmes de géométrie élémentaire. Méthodes. — Solutions. — Exemples PDF

By Javelot R.

Desk des matières :

Préliminaires
    I. — Problèmes usuels
    II. — Conseils
        a) Égalités d’angles
        b) Égalités de longueur
        c) Droites orthogonales
        d) Droites et plans perpendiculaires
        e) Droites parallèles
        f) Droites et plans parallèles
        g) Plans parallèles entre eux
        h) Plans perpendiculaires
        i) Droite et cercle tangents
        j) Sphère et plan tangents
    Exercices proposés avec symptoms pour les résoudre

Chap. I. — issues en ligne droite. — issues dans un même plan
    I. — issues en ligne droite
        Applications
    II. — issues dans un même plan
    Exercices proposés avec symptoms pour les résoudre
    Exercices proposés

Chap. II. — Droites concourantes, cercles concourants. — Plans passant par une même droite. — Droite dans un même plan
    I. — Droites concourantes, cercles concourants
    II. — Manières de prouver que des plans passent par une même droite
    III. — Manière de prouver que des droites sont dans un même plan
    Exercices proposés avec symptoms pour les résoudre
    Exercices proposés

Chap. III. — issues sur un même cercle. issues sur une même sphère
    Exercices proposés avec symptoms pour les résoudre
    Exercices proposés

Chap. IV. — Lieux géométriques
    Définition et généralités, conseils
    Applications
    Inversion
    Inversieurs de Peaucellier, Hart, Perrolaz, etc.
    De l’inversion comme moyen de recherche
    Lieux géométriques échappant en partie aux règles ci-dessus
        I. — Plan perpendiculaire à l. a. perpendiculaire commune de deux droites en son milieu
        II. — Problème de Lahire
        III. — Parallélogramme de Klérity
        IV. — Parallélogramme d’Ewans
    Exercices proposés avec symptoms pour les résoudre
    Exercices proposés

Chap. V. — Des structures de figures
    Généralités
    Méthode de substitution
    Méthode par intersection de lieux géométriques ou méthode par délaissement
    Méthode de réalisation
    Méthode des dilatations spéciale aux cercles
    Méthode des cercles ou des sphères de rayon nul
    Méthode des figures semblables
    Méthode des enveloppes
    Méthode par groupement particulier des éléments de l. a. figure
    Méthode par symétrie
    Méthode par homothétie
    Méthode par inversion
    Constructions échappant aux méthodes précédentes
    Exercices proposés avec symptoms pour les résoudre
    Exercices proposés

Chap. VI. — De l’exactitude ; exemples

Chap. VII. — kin métriques
    I. — Démonstration des égalités de los angeles forme : A × B = C × D; A × B = C²
    II. — Calcul d’une grandeur en fonction d’autres
    III. — Démonstration de l’égalité de deux grandeurs
    IV. — Méthode des aires
    V. — Méthode des volumes
    VI. — kin métriques diverses
    Exercices proposés avec symptoms pour les résoudre
    Exercices proposés

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Download E-books Normal Forms and Bifurcation of Planar Vector Fields PDF

By Shui-Nee Chow

This booklet is especially serious about the bifurcation concept of ODEs. Chapters 1 and a pair of of the e-book introduce systematic tools of simplifying equations: heart manifold thought and basic shape conception, through which one might lessen the measurement of equations and alter varieties of equations to be so simple as attainable. Chapters 3-5 of the e-book learn in enormous aspect the bifurcation of these one or dimensional equations with one, or numerous parameters.

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Download E-books Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals (Understanding Complex Systems) PDF

By Vladimir G. Ivancevic

Complex Nonlinearity: Chaos, part Transitions, Topology swap and direction Integrals is a ebook approximately prediction & regulate of normal nonlinear and chaotic dynamics of high-dimensional complicated platforms of assorted actual and non-physical nature and their underpinning geometro-topological swap.

The publication begins with a textbook-like reveal on nonlinear dynamics, attractors and chaos, either temporal and spatio-temporal, together with smooth recommendations of chaos–control. bankruptcy 2 turns to the sting of chaos, within the type of section transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), in addition to the comparable box of synergetics. whereas the normal degree for linear dynamics contains of flat, Euclidean geometry (with the corresponding calculation instruments from linear algebra and analysis), the traditional degree for nonlinear dynamics is curved, Riemannian geometry (with the corresponding instruments from nonlinear, tensor algebra and analysis). the extraordinary nonlinearity – chaos – corresponds to the topology swap of this curved geometrical level, often known as configuration manifold. bankruptcy three elaborates on geometry and topology swap in relation with advanced nonlinearity and chaos. bankruptcy four develops common nonlinear dynamics, non-stop and discrete, deterministic and stochastic, within the precise type of direction integrals and their action-amplitude formalism. This such a lot normal framework for representing either section transitions and topology switch begins with Feynman’s sum over histories, to be quick generalized into the sum over geometries and topologies. The final bankruptcy places all of the formerly constructed recommendations jointly and provides the unified type of complicated nonlinearity. the following now we have chaos, part transitions, geometrical dynamics and topology swap, all operating jointly within the kind of direction integrals.

The target of this publication is to supply a major reader with a major medical instrument that may permit them to truly practice a aggressive learn in glossy advanced nonlinearity. It encompasses a finished bibliography at the topic and a close index. aim readership contains all researchers and scholars of advanced nonlinear platforms (in physics, arithmetic, engineering, chemistry, biology, psychology, sociology, economics, medication, etc.), operating either in industry/clinics and academia.

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