Introduction to Tensor Analysis and the Calculus of Moving Surfaces

Filename: introduction-to-tensor-analysis-and-the-calculus-of-moving-surfaces.pdf
ISBN: 9781461478676
Release Date: 2013-09-24
Number of pages: 302
Author: Pavel Grinfeld
Publisher: Springer Science & Business Media

Download and read online Introduction to Tensor Analysis and the Calculus of Moving Surfaces in PDF and EPUB This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.


Tensoranalysis

Filename: tensoranalysis.pdf
ISBN: 9783110213218
Release Date: 2009-02-26
Number of pages: 462
Author: Heinz Schade
Publisher: Walter de Gruyter

Download and read online Tensoranalysis in PDF and EPUB Dieses Lehrbuch stellt eine umfassende und leicht verständliche Einführung in die Tensoranalysis dar, die hier als Oberbegriff von klassischer Tensoranalysis und Tensoralgebra zu verstehen ist und die in vielen Anwendungen der Physik und der Ingenieurwissenschaften benötigt wird. Es vermittelt die nötigen algebraischen Hilfsmittel und enthält zahlreiche Übungsaufgaben mit Lösungen, so dass es sich auch für ein Selbststudium eignet.


ber die Hypothesen welche der Geometrie zu Grunde liegen

Filename: ber-die-hypothesen-welche-der-geometrie-zu-grunde-liegen.pdf
ISBN: 9783662423165
Release Date: 2013-12-11
Number of pages: 50
Author: Bernhard Riemann
Publisher: Springer-Verlag

Download and read online ber die Hypothesen welche der Geometrie zu Grunde liegen in PDF and EPUB Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.


Raum Zeit Materie

Filename: raum-zeit-materie.pdf
ISBN: 9785880098026
Release Date: 1993
Number of pages:
Author: Hermann Weyl
Publisher: Рипол Классик

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Das Rad der Zeit

Filename: das-rad-der-zeit.pdf
ISBN: 3596145902
Release Date: 2001
Number of pages: 275
Author: Carlos Castaneda
Publisher:

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Lineare Algebra

Filename: lineare-algebra.pdf
ISBN: 9783642556319
Release Date: 2013-03-07
Number of pages: 656
Author: Gilbert Strang
Publisher: Springer-Verlag

Download and read online Lineare Algebra in PDF and EPUB Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.


Der Weg zur Wirklichkeit

Filename: der-weg-zur-wirklichkeit.pdf
ISBN: 3827423414
Release Date: 2010-04-20
Number of pages: 357
Author: Roger Penrose
Publisher: Spektrum Akademischer Verlag

Download and read online Der Weg zur Wirklichkeit in PDF and EPUB Der Weg zur Wirklichkeit ist eine Kurzübersetzung des Penrose-Klassikers "The Road to Reality", die aus dem Monumentalwerk für Physik- und Mathematikexperten die allgemeinverständlichen Kapitel für interessierte Laien lesbar macht. Wer ein Faible für die Grundfragen der Wissenschaft, einen Blick für Geometrie, einen Sinn für Zahlen und Neugier für kosmologische Theorien hat, findet in diesem klar und kompetent geschriebenen Buch überraschende und provozierende Ideen. Schulmathematik wie die Bruchrechnung oder der berühmte Pythagorassatz lassen sich auf dem Weg zur Wirklichkeit völlig neu entdecken - im Spannungsfeld zwischen platonischer Mathematik, physikalischer Welt und menschlichem Bewusstsein.


Die Ausdehnungslehre

Filename: die-ausdehnungslehre.pdf
ISBN: 3836402270
Release Date: 2006
Number of pages: 388
Author: Hermann Graßmann
Publisher:

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Prandtl F hrer durch die Str mungslehre

Filename: prandtl-f-hrer-durch-die-str-mungslehre.pdf
ISBN: 3528482095
Release Date: 2002
Number of pages: 704
Author: Ludwig Prandtl
Publisher:

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Die Grundlagen der Arithmetik

Filename: die-grundlagen-der-arithmetik.pdf
ISBN: 3150084253
Release Date: 1987-01
Number of pages: 159
Author: Gottlob Frege
Publisher:

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Differential Geometry

Filename: differential-geometry.pdf
ISBN: 1151506346
Release Date: 2011-06
Number of pages: 384
Author: Source: Wikipedia
Publisher: Books LLC, Wiki Series

Download and read online Differential Geometry in PDF and EPUB Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 342. Chapters: Sphere, Tangent space, Curvature, Symplectic manifold, Shape of the Universe, Gauss-Bonnet theorem, Pseudosphere, Diffeology, Connection form, Differential geometry of surfaces, Riemannian connection on a surface, Differentiable manifold, Affine connection, Metric tensor, Cartan connection, Atiyah-Singer index theorem, Holonomy, Symmetric space, Frenet-Serret formulas, Covariance and contravariance of vectors, Lie sphere geometry, List of nonlinear partial differential equations, Systolic geometry, Hopf fibration, Envelope, Lie derivative, Jet, Covariant derivative, Anti de Sitter space, Clifford analysis, Symmetry, Darboux frame, Instanton, Conformal geometry, Torsion tensor, Generalizations of the derivative, Generalized complex structure, Radius of curvature, Grassmannian, Frobenius theorem, Differential geometry of curves, Classification of manifolds, Moving frame, Calabi-Yau manifold, Covariant transformation, Affine curvature, Almost complex manifold, Principal bundle, Introduction to systolic geometry, Petrov classification, Directional derivative, Tensor field, Generalized flag variety, Affine differential geometry, Pullback, G-structure, Hilbert scheme, Spray, Affine focal set, Maurer-Cartan form, Nonholonomic system, Sine-Gordon equation, Finsler manifold, Dual curve, Gaussian curvature, Frame of a vector space, Calabi conjecture, Associated bundle, Evolute, Real projective space, Information geometry, K3 surface, Pushforward, Stiefel manifold, Ricci decomposition, Carath odory conjecture, Bogomolov-Miyaoka-Yau inequality, Second fundamental form, Calibrated geometry, Hilbert's theorem, Ruled surface, Pedal curve, Calculus of moving surfaces, Banach bundle, Tortuosity, Metric signature, Cartan's equivalence method, Double tangent bundle, Projective connection, Invariant differential operator, List of diff...


Differential Geometry for Physicists and Mathematicians

Filename: differential-geometry-for-physicists-and-mathematicians.pdf
ISBN: 9789814566414
Release Date: 2014-03-06
Number of pages: 312
Author: José G Vargas
Publisher: World Scientific

Download and read online Differential Geometry for Physicists and Mathematicians in PDF and EPUB This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative — almost like a story being told — that does not impede sophistication and deep results. It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas of mathematics that are of interest to physicists and mathematicians, but are largely overlooked. Among these is Clifford Algebra and its uses in conjunction with differential forms and moving frames. It opens new research vistas that expand the subject matter. In an appendix on the classical theory of curves and surfaces, the author slashes not only the main proofs of the traditional approach, which uses vector calculus, but even existing treatments that also use differential forms for the same purpose. Contents:Introduction:OrientationsTools:Differential FormsVector Spaces and Tensor ProductsExterior DifferentiationTwo Klein Geometries:Affine Klein GeometryEuclidean Klein GeometryCartan Connections:Generalized Geometry Made SimpleAffine ConnectionsEuclidean ConnectionsRiemannian Spaces and Pseudo-SpacesThe Future?:Extensions of CartanUnderstand the Past to Imagine the FutureA Book of Farewells Readership: Physicists and mathematicians working on differential geometry. Keywords:Differential Geometry;Differential Forms;Moving Frames;Exterior CalculusKey Features:Reader FriendlyNaturalnessRespect for the history of the subject and related incisiveness


The American Mathematical Monthly

Filename: the-american-mathematical-monthly.pdf
ISBN: UOM:39015024438502
Release Date: 1894
Number of pages:
Author:
Publisher:

Download and read online The American Mathematical Monthly in PDF and EPUB Includes section "Recent publications."


Announcement of Courses

Filename: announcement-of-courses.pdf
ISBN: UCAL:B3088613
Release Date: 1955
Number of pages:
Author: United States. National Bureau of Standards. Graduate School
Publisher:

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