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Cet ouvrage est une introduction élémentaire à la théorie des équations différentielles. Il est destiné à illustrer un cours classique sur les équations différentielles dans le cadre d'une licence de mathématiques, mais il peut également servir d'initiation aux notions de base indispensables aux applications. Une première partie est consacrée à des pré- requis de calcul différentiel et de topologie différentielle : définition des termes et notions de base utilisées par la suite, concernant aussi bien le calcul différentiel dans un espace euclidien que la topologie différentielle. La deuxième partie est la matière d'un cours classique sur les équations différentielles. Les champs linéaires et les propriétés générales des trajectoires sont donc évidemment exposés. Mais, dans la tradition initiée par Henri Poincaré, on insiste aussi sur les aspects qualitatifs du comportement des solutions, avec l'introduction de la notion de flot d'un champ de vecteurs, qui joue un rôle fondamental car elle sert de base à l'étude essentielle des propriétés de récurrence et de stabilité des orbites. La notion d'application de Poincaré d'une orbite périodique est développée et quelques résultats importants de la théorie qualitative sont démontrés. Les lecteurs trouveront un développement de cet ouvrage dans le tome II, publié dans la même collection (Vers la théorie des systèmes dynamiques).
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COMPUTER SOLUTION OF LARGE LINEAR SYSTEMSSTUDIES IN MATHEMATICS AND ITS APPLICATIONS VOLUME 28 (SMIA)
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This work deals with integrals in calculus which is a fundamental tool for mathematical analysis and for the calculation of probabilities. The work is divided into 11 chapters as follows: Computations using integrals, for example Lebesgue integration techniques as it applies to measurable real analysis, measurable spaces, for example Euclidean n-space, integrable functions defined on Rn, the calculations of Lebesgue-Stieltjes integration, their functions as defined by integrals, convolution, Fourier transform, Fourier series, the applications and their complements.
Calculus, Integral. --- Differential equations. --- 517.91 Differential equations --- Differential equations --- Integral calculus
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Ordinary differential equations --- Differential equations --- #TELE:SISTA --- Equations, Differential --- Bessel functions --- Calculus --- Differential equations. --- 517.91 Differential equations --- 517.91. --- Numerical solutions --- 517.91 --- Equations differentielles ordinaires
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Ordinary differential equations --- Differential equations --- Equations différentielles --- Differential equations. --- Equations, Differential --- Bessel functions --- Calculus --- 517.91 Differential equations --- Equations différentielles --- 517.91. --- Numerical solutions --- 517.91
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Ordinary differential equations --- Differential equations --- Numerical solutions --- 517.91 --- -Equations, Differential --- Bessel functions --- Calculus --- Ordinary differential equations: general theory --- Numerical solutions. --- -517.91 Differential equations --- 517.91 Ordinary differential equations: general theory --- -Ordinary differential equations: general theory --- -517.91 Ordinary differential equations: general theory --- 517.91 Differential equations --- Numerical solutions&delete& --- Differential equations - Numerical solutions
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Ergodic theory. Information theory --- Ordinary differential equations --- Differential equations --- Topological dynamics --- #TELE:SISTA --- Dynamics, Topological --- Differentiable dynamical systems --- Equations, Differential --- Bessel functions --- Calculus --- 517.91 Differential equations --- 517.91. --- Numerical solutions --- 517.91
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Ordinary differential equations --- Differential equations --- differentiaalvergelijkingen --- design --- stelsels --- benaderen --- Laplace transformatie --- lineair --- runge-kutta --- model --- numeriek --- Equations, Differential --- Bessel functions --- Calculus --- 517.91 Differential equations --- 517.91. --- Numerical solutions --- 517.91
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Ordinary differential equations --- Numerical solutions of differential equations --- Differential equations --- Equations différentielles --- Numerical solutions --- Solutions numériques --- Equations différentielles --- Solutions numériques --- 517.91 Differential equations --- 517.91 --- Numerical solutions. --- Monograph --- Numerical solutions&delete& --- Differential equations - Numerical solutions
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Differential equations in abstract spaces
Banach spaces. --- Differential equations. --- Nonlinear operators. --- Operators, Nonlinear --- 517.91 Differential equations --- Differential equations --- Operator theory --- Functions of complex variables --- Generalized spaces --- Topology --- Banach spaces --- Nonlinear operators --- 517.91 --- Numerical solutions
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