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6 Remote Warehouse Mathematics- Differential Equations

Differential Forms with Applications to the Physical Sciences

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Differential Forms with Applications to the Physical Sciences Cover

 

Synopses & Reviews

Publisher Comments:

"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." — 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.

"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." — F. E. J. Linton, Wesleyan University, American Mathematical Monthly.

Synopsis:

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.

Synopsis:

A graduate-level text introducing 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. Directed primarily to graduate-level engineers and physical scientists, it has also been used successfully to introduce modern differential geometry to graduate students in mathematics. Includes 45 illustrations. Index.

Table of Contents

  Foreword; Preface to the Dover Edition; Preface to the First Edition

I. Introduction

  1.1 Exterior Differential Forms

  1.2 Comparison with Tensors

II. 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 Problems

III. 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 Problems

IV. 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 Problems

V. 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 Problems

VI. 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 Law

VII. 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 Theorem

VIII. 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 Problems

IX. 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 Problems

X. 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

Product Details

ISBN:
9780486661698
Author:
Flanders, Harley
Publisher:
Dover Publications
Author:
Mathematics
Author:
Harley Fland
Author:
ers
Location:
Mineola, N.Y. :
Subject:
Science
Subject:
Physics
Subject:
Differential Equations
Subject:
Mathematical Physics
Subject:
Differential forms
Subject:
General Mathematics
Subject:
Applied
Subject:
Mathematics-Differential Equations
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
3686
Publication Date:
19891231
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
240
Dimensions:
8.5 x 5.38 in 0.56 lb

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Related Subjects


Reference » Science Reference » General
Science and Mathematics » Chemistry » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Physics » General

Differential Forms with Applications to the Physical Sciences New Trade Paper
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Product details 240 pages Dover Publications - English 9780486661698 Reviews:
"Synopsis" by ,
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.
"Synopsis" by ,
A graduate-level text introducing 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. Directed primarily to graduate-level engineers and physical scientists, it has also been used successfully to introduce modern differential geometry to graduate students in mathematics. Includes 45 illustrations. Index.
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