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Stories About Maxima And Minima
by Tikhomirov,
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This book aims to acquaint the reader with the whole circle of ideas and provide an understanding of how and why a mathematical theory is born. In Part I the reader will get to know many concrete problems and, in the course of the discussion of
their solutions, will get to know the creative work of some of the best mathematicians of the past. In Part II the author introduces a method to solve maximum and minimum problems that originated with Lagrange and concludes by solving all the problems that are
dealt with in Part I (problems marked by the dissimilarity of their solutions) by means of a single general method, in a standard way, by using one and the same solution.* Contents Part I: Ancient maximum and minimum problems: Why do we solve maximum and minimum problems?; The oldest problem—Dido’s problem; Maxima and minima in nature; Maxima and minima in geometry; Maxima and minima in algebra and in analysis; Kepler’s problem; The Brachistochrone; Newton’s aerodynamical problem; Part II: Methods of solution of extremal problems: What is a function?; What is an extremal problem?; Extrema of unctions of one variable; Extrema of functions of many variables: the Lagrange principle; More problem solving; What happened later in the theory of extremal problems?; More accurately, a
discussion; Bibliography. 200pp. (1998) 230 × 150mm ISBN 97881 7371 1213
Pages : 200
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