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Kernel functions and differential equations
Differential equations, Partial. --- Differential equations. --- Functions. --- Analysis (Mathematics) --- Differential equations --- Mathematical analysis --- Mathematics --- Numbers, Complex --- Set theory --- Calculus --- 517.91 Differential equations --- Partial differential equations
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Mathematical development, the author of this text observes, comes about through specific, easily understood problems that require difficult solutions and demand the use of new methods. Richard Courant employs this instructive approach in a text that balances the individuality of mathematical objects with the generality of mathematical methods. Beginning with a discussion of Dirichlet's principle and the boundary-value problem of potential theory, the text proceeds to examinations of conformal mapping on parallel-slit domains and Plateau's problem. Succeeding chapters explore the general problem of Douglas and conformal mapping of multiply connected domains, concluding with a survey of minimal surfaces with free boundaries and unstable minimal surfaces -- 4e de couverture
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Differential equations, Elliptic. --- Dirichlet problem. --- Équations différentielles elliptiques. --- Dirichlet, Problème de --- Fonctions d'une variable complexe --- Methodes variationnelles --- Geometrie differentielle classique --- Theorie du potentiel --- Equations aux derivees partielles elliptiques --- Representation conforme --- Surfaces minima
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The Role of Mathematics in Science aims to illustrate the many ways in which mathematical methods have helped discovery in science. It is aimed at a group of readers who are interested in mathematics beyond the level of high school. The authors occasionally use some calculus and more intricate arguments. The book should appeal to college students and general readers with some background in mathematics. The authors state that, 'If we succeed in giving an impression of the beauty and power of mathematical reasoning in science, the purpose of our work will have been achieved.' This book includes the laws of levers and inclined planes, the laws of exponential versus limited population growth, ray optics, and relativity.
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