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Differential Forms with Applications to the Physical Sciences
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Harley Flanders
A graduate-level text utilizing exterior differential forms in the analysis of a variety of mathematical problems in the physical and engineering sciences. Includes 45 illustrations. Index.
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Differential Forms in Algebraic Topology
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Raoul Bott, Loring W Tu
This text, developed from a first-year graduate course in algebraic topology, is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas- de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes-and include some ...
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Tensors, Differential Forms, and Variational Principles
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David Lovelock
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
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A Geometric Approach to Differential Forms
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David Bachman
The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the sophomore undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The ...
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Differential Forms and Applications
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Manfredo P Do Carmo
The book treats differential forms and uses them to study some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely the ...
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Differential forms a complement to vector calculus
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Weintraub
This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable ...
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From Calculus to Cohomology: de Rham Cohomology and Characteristic Classes
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IB Madsen, Jergen Tornehave, Jorgen Tornehave
De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of open sets in Euclidean ...
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Curvature and Characteristic Classes
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J L DuPont
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Differential forms
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by
Henri Cartan
Addressed to 2nd- and 3rd-year students, this work by a world-famous teacher skillfully spans the pure and applied branches, so that applied aspects gain in rigor while pure mathematics loses none of its dignity. Equally essential as a text, a reference, or simply as a brilliant mathematical exercise. 1971 edition.
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Differential Forms Orthogonal to Holomorphic Functions or Forms, and Their Properties
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Global Analysis: Differential Forms in Analysis, Geometry, and Physics
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by
Ilka Agricola, Alan Forrest
This book is an introduction to differential geometry through differential forms, emphasizing their applications in various areas of mathematics and physics. Well-written and with plenty of examples, this textbook originated from courses on geometry and analysis and presents a widely-used mathematical technique in a lucid and very readable style. ...
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Differential Forms on Singular Varieties: de Rham and Hodge Theory Simplified
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by
Vincenzo Ancona, Bernard Gaveau
Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of higher ...
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Geometry to Differential Forms
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by
S. Morita
Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, ...
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Differentiable Manifolds
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by
Yozo Matsushima
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Differential Forms: A Heuristic Introduction
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Morris Schreiber
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Differentiable Manifolds and Quadratic Forms
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Friedrich Hirzebruch, W. Neumann
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Differential forms on electromagnetic networks
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N. V. Balasubramanian
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Multivectors and Clifford Algebra in Electrodynamics
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Bernard Jancewicz
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The General Stokes' Theorem
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Helmut Grunsky
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Traces of differential forms and Hochschild homology
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Hübl
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Cohomology and Differential Forms
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by
Izu Vaisman
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Invariant Forms on Grassmann Manifolds
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by
Wilhelm Stoll
Most of the results in this monograph are known. The method of proof is new, especially in the case of Matsushima's theorem. The topic is not easily accessible. Therefore an introduction has been written here in order to provide a clear, coherent, intransically formulated account which will be useful for applications to value distribution theory, ...
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Heat Kernels and Dirac Operators
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Nicole Berline
The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recent generalizations, are presented. The formula for the index of the Dirac operator is obtained from the classical formula for the heat kernel of the harmonic ...
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Differential Forms in Electromagnetics
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Ismo V Lindell
This book offers an introduction to multivectors, dyadics, and differential forms for electrical engineers. While physicists have long applied differential forms to various areas of theoretical analysis, dyadic algebra is also the most natural language for expressing electromagnetic phenomena mathematically. George Deschamps pioneered the ...
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Invariants of Quadratic Differential Forms
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Joseph Edmund Wright
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