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Dieser Titel aus dem De Gruyter-Verlagsarchiv ist digitalisiert worden, um ihn der wissenschaftlichen Forschung zugänglich zu machen. Da der Titel erstmals im Nationalsozialismus publiziert wurde, ist er in besonderem Maße in seinem historischen Kontext zu betrachten. Mehr erfahren Sie .› This title from the De Gruyter Book Archive has been digitized in order to make it available for academic research. It was originally published under National Socialism and has to be viewed in this historical context. Learn more .›

Calculus --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Study and teaching.

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Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radó. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The fourth edition gives a survey on new developments in the field. In particular it includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up. Also the recently discovered results for backward bubbling in the heat flow for harmonic maps or surfaces are discussed. Aside from these more significant additions, a number of smaller changes throughout the text have been made and the references have been updated.

Mathematics. --- Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Global analysis (Mathematics). --- Systems theory. --- Mathematical optimization. --- Mathématiques --- Analyse globale (Mathématiques) --- Optimisation mathématique --- Calculus of variations. --- Differential equations, Nonlinear. --- Hamiltonian systems. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Nonlinear differential equations --- Isoperimetrical problems --- Variations, Calculus of --- Mathematical analysis. --- Analysis (Mathematics). --- System theory. --- Maxima and minima --- Differentiable dynamical systems --- Nonlinear theories --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Systems, Theory of --- Systems science --- Science --- Philosophy --- 517.1 Mathematical analysis --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal