Calculus of variations in mathematical physics

H. A Lauwerier

This tract represents worked-out lecture notes of a course in the calculus of variations delivered by the author to students in mathematical physics at the University of Amsterdam. In this course the calcucalculus of variations is treated in a slightly modernized way by making full use of the language of vector spaces. Although the reader is supposed to be familiar with the fundamental notions of a Banach space and a Hilbert space, two sections are included in which these spaces are treated systematically in a condensed fashion. Much attention is paid to problems of theoretical mechanics including Noether’s theorem. Some elementary knowledge of boundary value problems, e.g. vibrating string and membrane, will enable the reader to appreciate more fully those parts of the text, in which applications of Hilbert space theory are made. Much material for this course is derived from the books by Gelfand and Fomin and by Michlin. In particular, the first book represents an easily readable modern introduction to the calculus of variations and its applications.