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Editore: Springer New York Nov 1984, 1984
ISBN 10: 0387960597ISBN 13: 9780387960593
Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germania
Libro Print on Demand
Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f EUR F, (1) Au = f, where A: DA C U + F is an operator with a non-empty domain of definition D , in a metric space U, with range in a metric space F. The metrics A on U and F will be denoted by P and P ' respectively. Relative u F to the twin spaces U and F, J. Hadamard P-06] gave the following defini tion of correctness: the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are satisfied: (1) The range of the value Q of the operator A coincides with A F ('sol vabi li ty' condition); (2) The equality AU = AU for any u ,u EUR DA implies the I 2 l 2 equality u = u ('uniqueness' condition); l 2 (3) The inverse operator A-I is continuous on F ('stability' condition). Any reasonable mathematical formulation of a physical problem requires that conditions (1)-(3) be satisfied. That is why Hadamard postulated that any 'ill-posed' (improperly posed) problem, that is to say, one which does not satisfy conditions (1)-(3), is non-physical. Hadamard also gave the now classical example of an ill-posed problem, namely, the Cauchy problem for the Laplace equation. 280 pp. Englisch.
Editore: Springer New York Nov 1984, 1984
ISBN 10: 0387960996ISBN 13: 9780387960999
Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germania
Libro Print on Demand
Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This curriculum and its description were developed during the period 1981 - 1984 216 pp. Englisch.
Editore: Springer New York Nov 1984, 1984
ISBN 10: 0387960309ISBN 13: 9780387960302
Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germania
Libro Print on Demand
Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book is the result of a decision taken in 1980 to begin studying the history of mathematics in the nineteenth century. I hoped by doing it to learn some thing of value about Kovalevskaya herself and about the mathematical world she inhabited. Having been trained as a mathematician, I also hoped to learn something about the proper approach to the history of the subject. The decision to begin the study with Kovalevskaya, apart from the intrinsic interest of Kovalevskaya herself, was primarily based upon the fact that the writing on her in English had been done by people who were interested in sociological and psychological aspects of her life. None of these writings discussed her mathematical work in much detail. This omission seemed to me a serious one in biographical studies of a woman whose primary significance was her mathematical work. In regard to both the content of nineteenth century mathematics and the nature of the history of mathematics I learned a great deal from writing this book. The attempt to put Kovalevskaya's work in historical context involved reading dozens of significant papers by great mathematicians. In many cases, I fear, the purport of these papers is better known to many of my readers than to me. If I persevered despite misgivings, my excuse is that this book is, after all, primarily about Kovalevskaya. If specialists in Euler, Cauchy, etc. 260 pp. Englisch.
Editore: Springer New York Nov 1984, 1984
ISBN 10: 038790915XISBN 13: 9780387909158
Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germania
Libro Print on Demand
Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional analysis and its applications. In doing this, I have recommended to my students a number of excellent monographs devoted to specialized topics, but there was no complete survey-type exposition of nonlinear functional analysis making available a quick survey to the wide range of readers including mathematicians, natural scientists, and engineers who have only an elementary knowledge of linear functional analysis. I have tried to close this gap with my five-part lecture notes, the first three parts of which have been published in the Teubner-Texte series by Teubner-Verlag, Leipzig, 1976, 1977, and 1978. The present English edition was translated from a completely rewritten manuscript which is significantly longer than the original version in the Teubner-Texte series. The material is organized in the following way: Part I: Fixed Point Theorems. Part II: Monotone Operators. Part III: Variational Methods and Optimization. Parts IV jV: Applications to Mathematical Physics. The exposition is guided by the following considerations: (a) What are the supporting basic ideas and what intrinsic interrelations exist between them (/3) In what relation do the basic ideas stand to the known propositions of classical analysis and linear functional analysis ( y) What typical applications are there Vll Preface viii Special emphasis is placed on motivation. 688 pp. Englisch.