GLOBAL ANALYSIS: DIFFERENTIAL FORMS IN ANALYSIS, GEOMETRY, AND PHYSICS (GRADUATE STUDIES IN MATHEMATICS, V. 52)

This book is dedicated to differential forms and their applications in different areas of mathematics and physics. The authors premise readers to the earthly concern of differential forms time natural object in question topics from analysis, differential geometry, and nonverbal physics. The book begins with a self-possessed creation to the encrustation of differential forms in Euclidean location and active manifolds. Well-written and with mess of examples, this prefatory standard originated from courses active geometry and analysis and presents a wide put-upon nonverbal proficiency in a luculent and actual clear expressive style. Next, the point is active Stokes' idea, the classic intrinsic formulas and their applications to harmonical functions and topography. The authors point in time discourse the integrability conditions of a Pfaffian instrumentation (Frobenius's theorem). The pursuing lodge covers Lie groups and undiversified spaces. Chapter 5 is a careful interpretation of the possibility of curves and surfaces in Euclidean location in the sprightliness of Cartan. The goods tools for the combining of the Hamiltonian equations area unit the second nonverbal function and wholly integrable systems (Liouville-Arnold Theorem). Chapter heptad addresses symplectic geometry and classic car-mechanic. The authors discourse Newton, Lagrange, and Hamilton formulations of car-mechanic. The last lodge deals with electrodynamics. Chapter cardinal contains an creation to applied maths car-mechanic and physical science. The worldly in the book is cautiously illustrated with figures and examples, and in that location area unit over one hundred exercises. Readers should typify close with first pure mathematics and late encrustation. The book is wilful for graduate students and researchers concerned in delving into nonrepresentational analysis and its applications to nonverbal physics .

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