Enzyklopädie des Stiftungswesens in mittelalterlichen Gesellschaften
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The second part of "Local Analysis" is wholly based on the first one and provides a detailed introduction to the initial value problems of certain systems of first order ordinary and partial differential equations as well as to the theory of differential forms. The latter ones are given a concrete meaning in that the differentials are interpreted as elements of the dual basis whereby the differential forms turn out to be basis representations of alternating covariant tensor fields. Purely algebraic and analytic investigations are kept apart strictly from each other. The book aims at Pfaff's problem for which the maximal dimension of integral surfaces of a linear functional field is determined. And since the Cauchy-Kowaleski theorem is not applied, the occuring functions need not be assumed analytic but merely continuously differentiable a sufficiently large mnumber of times.
Part 1 Explicit systems of first order ordinary differential equations: existence and uniqueness theorem of Picard-Lindeloef; elementary methods for solving first order differential equations; linear systems; dependence of the solutions on a parameter. Part 2 Systems of first order partial differential equations: existence, uniqueness and dependence theorem for completely explicit systems; theory of characteristics for incompletely explicit systems with one unknown function; quasilinear systems. Part 3 Alternating multilinear functionals and operators: E. Cartan's exterior and differential forms; algebraic and analytic properties. Part 4 Alternating multilinear operator fields: integrating operators of subjective linear operator fields; associated and characteristic fields of an alternating multilinear operator field; Pfaff's problem.
| Zusatzinfo | Enthält eine Printausgabe und ein eBook |
|---|---|
| Verlagsort | Weinheim |
| Sprache | deutsch |
| Themenwelt | Geschichte ► Allgemeine Geschichte ► Mittelalter |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| ISBN-13 | 9783055016455 / 9783055016455 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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