Differential Forms with Applications to the Physical Sciences (eBook)
240 Seiten
Dover Publications (Verlag)
978-0-486-13961-6 (ISBN)
"e;To the reader who wishes to obtain a bird's-eye view of the theory of differential forms with applications to other branches of pure mathematics, applied mathematic and physics, I can recommend no better book."e; — T. J. Willmore, London Mathematical Society Journal.This excellent text introduces the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Requiring familiarity with several variable calculus and some knowledge of linear algebra and set theory, it is directed primarily to engineers and physical scientists, but it has also been used successfully to introduce modern differential geometry to students in mathematics.Chapter I introduces exterior differential forms and their comparisons with tensors. The next three chapters take up exterior algebra, the exterior derivative and their applications. Chapter V discusses manifolds and integration, and Chapter VI covers applications in Euclidean space. The last three chapters explore applications to differential equations, differential geometry, and group theory."e;The book is very readable, indeed, enjoyable — and, although addressed to engineers and scientists, should be not at all inaccessible to or inappropriate for ... first year graduate students and bright undergraduates."e; — F. E. J. Linton, Wesleyan University, American Mathematical Monthly.
Foreword; Preface to the Dover Edition; Preface to the First EditionI. Introduction 1.1 Exterior Differential Forms 1.2 Comparison with TensorsII. Exterior algebra 2.1 The Space of p-vectors 2.2 Determinants 2.3 Exterior Products 2.4 Linear Transformations 2.5 Inner Product Spaces 2.6 Inner Products of p-vectors 2.7 The Star Operator 2.8 ProblemsIII. The Exterior Derivative 3.1 Differential Forms 3.2 Exterior Derivative 3.3 Mappings 3.4 Change of coordinates 3.5 An Example from Mechanics 3.6 Converse of the Poincaré Lemma 3.7 An Example 3.8 Further Remarks 3.9 ProblemsIV. Applications 4.1 Moving Frames in E superscript 3 4.2 Relation between Orthogonal and Skew-symmetric Matrices 4.3 The 6-dimensional Frame Space 4.4 The Laplacian, Orthogonal Coordinates 4.5 Surfaces 4.6 Maxwell's Field Equations 4.7 ProblemsV. Manifolds and Integration 5.1 Introduction 5.2 Manifolds 5.3 Tangent Vectors 5.4 Differential Forms 5.5 Euclidean Simplices 5.6 Chains and Boundaries 5.7 Integration of Forms 5.8 Stokes' Theorem 5.9 Periods and De Rham's Theorems 5.10 Surfaces; Some Examples 5.11 Mappings of Chains 5.12 ProblemsVI. Applications in Euclidean Space 6.1 Volumes in E superscript n 6.2 Winding Numbers, Degree of a Mapping 6.3 The Hopf Invariant 6.4 Linking Numbers, the Gauss Integral, Ampère's LawVII. Applications to Different Equations 7.1 Potential Theory 7.2 The Heat Equation 7.3 The Frobenius Integration Theorem 7.4 Applications of the Frobenius Theorem 7.5 Systems of Ordinary Equations 7.6 The Third Lie TheoremVIII. Applications to Differential Geometry 8.1 Surfaces (Continued) 8.2 Hypersurfaces 8.3 Riemannian Geometry, Local Theory 8.4 Riemannian Geometry, Harmonic Integrals 8.5 Affine Connection 8.6 ProblemsIX. Applications to Group Theory 9.1 Lie Groups 9.2 Examples of Lie Groups 9.3 Matrix Groups 9.4 Examples of Matrix Groups 9.5 Bi-invariant Forms 9.6 ProblemsX. Applications to Physics 10.1 Phase and State Space 10.2 Hamiltonian Systems 10.3 Integral-invariants 10.4 Brackets 10.5 Contact Transformations 10.6 Fluid Mechanics 10.7 Problems Bibliography; Glossary of Notation; Index
Erscheint lt. Verlag | 26.4.2012 |
---|---|
Reihe/Serie | Dover Books on Mathematics |
Sprache | englisch |
Maße | 140 x 140 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
ISBN-10 | 0-486-13961-1 / 0486139611 |
ISBN-13 | 978-0-486-13961-6 / 9780486139616 |
Haben Sie eine Frage zum Produkt? |
Kopierschutz: Adobe-DRM
Adobe-DRM ist ein Kopierschutz, der das eBook vor Mißbrauch schützen soll. Dabei wird das eBook bereits beim Download auf Ihre persönliche Adobe-ID autorisiert. Lesen können Sie das eBook dann nur auf den Geräten, welche ebenfalls auf Ihre Adobe-ID registriert sind.
Details zum Adobe-DRM
Dateiformat: EPUB (Electronic Publication)
EPUB ist ein offener Standard für eBooks und eignet sich besonders zur Darstellung von Belletristik und Sachbüchern. Der Fließtext wird dynamisch an die Display- und Schriftgröße angepasst. Auch für mobile Lesegeräte ist EPUB daher gut geeignet.
Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen eine
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen eine
Geräteliste und zusätzliche Hinweise
Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.
aus dem Bereich