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In 1894 Ernst Zermelo published his doctoral dissertation from the University of Berlin, written under the direction of Hermann Amandus Schwarz and devoted to a study of Karl Weierstrass's methods in the calculus of variations. In an introductory note Zermelo states that he had become familiar with the contents of Weierstrass's lectures in 1892 from the copy in the "Mathematische Verein" in Berlin, as well as from a lecture given by Schwarz. Weierstrass had investigated the simplest case in which only the first derivatives of the variables appear in the variational integrand function. Zermelo's main goal is to extend Weierstrass's results on necessary and sufficient conditions involving the "excess' or E function (the material in the twentieth to the twenty-third lectures of Weierstrass's lectures as they were eventually published (1927)) to variational problems in parametric form in which the integrand contains derivatives of order higher than one

DOI: 10.1007/978-3-540-70856-8_2

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