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Exponential functions. --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions

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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.

Exponential functions. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions

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Fonctions exponentielles --- Fonctions logarithmes --- Functies [Exponentiele ] --- Functions [Exponential ] --- Functions [Hyperbolic ] --- Functions [Logarithmic ] --- Logarithmic functions --- Logaritmische functies --- Trigonometrical functions --- Mathematics --- Exponential functions --- Fonctions trigonométriques --- Mathématiques --- Study and teaching --- Étude et enseignement --- Fonctions exponentielles. --- Fonctions logarithmes. --- Fonctions trigonométriques. --- Étude et enseignement.

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A detailed exposition, with applications to problems in potential theory and quantum field theory.

Green's functions. --- Exponential functions. --- Mathematical physics. --- Physical mathematics --- Physics --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Mathematics

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The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .

Nonlinear systems. --- Exponential functions. --- Functions, Exponential --- Hyperbolic functions --- Systems, Nonlinear --- Mathematics. --- Fourier analysis. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Mathematical physics. --- Partial Differential Equations. --- Fourier Analysis. --- Mathematical Physics. --- Applications of Mathematics. --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- System theory --- Differential equations, partial. --- Math --- Science --- Analysis, Fourier --- Mathematical analysis --- Partial differential equations --- Engineering --- Engineering analysis --- Physical mathematics --- Physics --- Mathematics