Functional Analysis in Mechanics - Lebedev, L. P. (Springer New York, 2003)
Technological University for assisting with the English translation, for p- ducing the LaTeX ?les, and for contributing the problem hints that appear in the Appendix. Department of Mechanics and Mathematics L.P. Lebedev Rostov State University, Russia & Department of Mathematics National University of Colombia, Colombia Department of Mechanics and Mathematics I.I. Vorovich Rostov State University, Russia PrefacetotheRussianEdition This is an extended version of a course of lectures we have given to third and fourth year students of mathematics and mechanics at Rostov State University. Our lecture audience typically includes students of applied - chanics and engineering. These latter students wish to master methods of contemporary mathematics in order to read the scienti?c literature, j- tify the numerical and analytical methods they use, and so on; they lack enthusiasmforcoursesinwhichapplicationsappearonlyafterlongunint- rupted stretches of theory. Finally, the audience includes mathematicians. These listeners, already knowing more functional analysis than the course has to o?er, are interested only in applications. In order to please such a diverseaudience,wehavehadtoarrangethecoursecarefullyandintroduce sensible applications from the beginning. The brevity of the course — and the boundless extent of functional analysis — force us to present only those topicsessentialtothechosenapplications.Wedo,however,trytomakethe course self-contained and to cover the foundations of functional analysis
Keywords: Mathematics; Functional analysis; Differential equations, partial; Mechanics; Materials; Functional Analysis; Partial Differential Equations; Continuum Mechanics and Mechanics of Materials; Mathematik; Kontinuumsmechanik; Metrischer Raum; Angewandte Mathematik; Operatortheorie; Funktionalanalysis; Mechanik