Differential Forms. Theory and Practice

✍ Scribed by Steven H. Weintraub (Auth.)

Publisher: Academic Press
Year: 2014
Tongue: English
Leaves: 398
Edition: 2
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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, 2^nd 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.

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

✦ Table of Contents

Content:
Differential Forms, Page i
Differential Forms, Page iii
Copyright, Page iv
Dedication, Page v
Preface, Pages ix-xi
Chapter 1 - Differential Forms in , I, Pages 1-50
Chapter 2 - Differential Forms in , II, Pages 51-99
Chapter 3 - Push-forwards and Pull-backs in , Pages 101-140
Chapter 4 - Smooth Manifolds, Pages 141-206
Chapter 5 - Vector Bundles and the Global Point of View, Pages 207-226
Chapter 6 - Integration of Differential Forms, Pages 227-307
Chapter 7 - The Generalized Stokes’s Theorem, Pages 309-359
Chapter 8 - de Rham Cohomology, Pages 361-391
Index, Pages 393-395

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