Differential Forms

Differential Forms, 2nd Edition

Theory and Practice

Differential Forms, 2nd Edition,Steven Weintraub,ISBN9780123944030


Academic Press




229 X 152

Put the theory into practice with this informative and accessible reference that teaches you how differential forms can be used as a powerful computational tool in analyzing and solving research problems.

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Key Features

  • The only reference that provides a solid theoretical basis of how to develop and apply differential forms to real research problems
  • Includes computational methods for graphical results essential for math modeling
  • Presents common industry techniques in detail for a deeper understanding of mathematical applications
  • Introduces theoretical concepts in an accessible manner


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.


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

Steven Weintraub

Steven H. Weintraub is a Professor of Mathematics at Louisiana State University. He received his Ph.D. from Princeton University, and has been at LSU since that time, with temporary leaves to UCLA, Rutgers, Oxford, Yale, Gottingen, Bayreuth, and Hannover (Germany).Professor Weintraub is a member of the American Mathematical Society and a former member of the Council of the AMS. He has written more than 40 research papers and two other books: a graduate algebra book and a reserach monograph.

Affiliations and Expertise

Louisiana State University, Baton Rouge, USA

Differential Forms, 2nd Edition

Differential Forms
The Algrebra of Differential Forms
Exterior Differentiation
The Fundamental Correspondence
Oriented Manifolds
The Notion Of A Manifold (With Boundary)

Differential Forms Revisited
Push-Forwards And Pull-Backs

Integration Of Differential Forms Over Oriented Manifolds
The 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' Theorem
Statement Of The Theorem
The Fundamental Theorem Of Calculus And Its Analog For Line Integrals
Green's And Stokes' Theorems
Gauss's Theorem
Proof of the GST

For The Advanced Reader
Differential Forms In IRN And Poincare's Lemma
Manifolds, Tangent Vectors, And Orientations
The Basics of De Rham Cohomology

Answers To Exercises
Subject Index

Quotes and reviews

"This is a rigorous and well-written treatment of differential forms with a careful and detailed progression from very basic notions."--MAA.org, 24-Sep-14

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