Differential Forms book cover

Differential Forms

Theory and Practice

Differential forms are utilized as a mathematical technique to help students, researchers, and engineers analyze and interpret problems where abstract spaces and structures are concerned, and when questions of shape, size, and relative positions are involved. Differential Forms has gained high recognition in the mathematical and scientific community as a powerful computational tool in solving research problems and simplifying very abstract problems through mathematical analysis on a computer. Differential Forms, 2nd Edition, is a solid resource for students and professionals needing a solid general understanding of the mathematical theory and be able to apply that theory into practice. Useful applications are offered to investigate a wide range of problems such as engineers doing risk analysis, measuring computer output flow or testing complex systems. They can also be used to determine the physics in mechanical and/or structural design to ensure stability and structural integrity. The book offers many recent examples of computations and research applications across the fields of applied mathematics, engineering, and physics.

Audience

Graduate students in mathematics, engineering and physics; Engineers, Physicists, Applied Mathematicians

Hardbound, 408 Pages

Published: February 2014

Imprint: Academic Press

ISBN: 978-0-12-394403-0

Contents

  • Differential FormsThe Algrebra of Differential FormsExterior DifferentiationThe Fundamental Correspondence Oriented ManifoldsThe Notion Of A Manifold (With Boundary)Orientation Differential Forms Revisitedl-FormsK-FormsPush-Forwards And Pull-Backs Integration Of Differential Forms Over Oriented ManifoldsThe Integral Of A 0-Form Over A Point (Evaluation)The Integral Of A 1-Form Over A Curve (Line Integrals)The Integral Of A2-Form Over A Surface (Flux Integrals)The Integral Of A 3-Form Over A Solid Body (Volume Integrals)Integration Via Pull-Backs The Generalized Stokes' TheoremStatement Of The TheoremThe Fundamental Theorem Of Calculus And Its Analog For Line IntegralsGreen's And Stokes' TheoremsGauss's TheoremProof of the GST For The Advanced ReaderDifferential Forms In IRN And Poincare's LemmaManifolds, Tangent Vectors, And OrientationsThe Basics of De Rham Cohomology AppendixAnswers To ExercisesSubject Index

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