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This monograph is the first published book devoted to the theory of differential equations with non-instantaneous impulses. It aims to equip the reader with mathematical models and theory behind real life processes in physics, biology, population dynamics, ecology and pharmacokinetics. The authors examine a wide scope of differential equations with non-instantaneous impulses through three comprehensive chapters, providing an all-rounded and unique presentation on the topic, including: - Ordinary differential equations with non-instantaneous impulses (scalar and n-dimensional case) - Fractional differential equa tions with non-instantaneous impulses (with Caputo fractional derivatives of order q ϵ (0, 1)) - Ordinary differential equations with non-instantaneous impulses occurring at random moments (with exponential, Erlang, or Gamma distribution) Each chapter focuses on theory, proofs and examples, and contains numerous graphs to enrich the reader’s understanding. Additionally, a carefully selected bibliography is included. Graduate students at various levels as well as researchers in differential equations and related fields will find this a valuable resource of both introductory and advanced material.

Mathematics. --- Differential equations. --- Partial differential equations. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Impulsive differential equations. --- Impulse differential equations --- Impulsive partial differential equations --- Differential equations, Partial --- Differential equations, partial. --- Differential Equations. --- 517.91 Differential equations --- Differential equations --- Partial differential equations

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Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.

Differential equations. --- 517.91 Differential equations --- Differential equations

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Refusant tout élitisme, André Ronveaux, professeur à l'Université de Montréal, a voulu s’adresser dés les années soixante aux élèves de l’enseignement secondaire, âgés de 16 à 18 ans, ou aux étudiants universitaires dont la formation mathématique n’est pas très poussée. Les publications reproduites dans cet ouvrage témoigne de sa conviction que l’on peut apprendre de belles et profondes méthodes mathématiques sans beaucoup de bagage initial et à partir d’exemples concrets, aisément compréhensibles, enracinés dans des applications intéressantes et cela sans sacrifier à la rigueur mais en donnant le goût d’en savoir plus.Le contenu de ces livres repose sur une véritable pratique innovante en pédagogie puisque l’auteur a eu l’occasion d’expérimenter avec succès l’enseignement de ce contenu lors de cours délivrés durant un « camp mathématique » à Joliette (Québec) en juillet 1965.« Dans cette perspective, il me semble que les professeurs pourraient essayer d’introduire la matière et la pédagogie spécifique du fascicule Modèles déterministes en Sciences Humaines au sein d’un cours de mathématiques pour biologistes, médecins, économistes, mais aussi chimistes. » (D. Lambert, UNamur)

Differential equations --- Problems, exercises, etc. --- Difference equations

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Integral equations --- Volterra equations --- Functional analysis

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This monograph is the first published book devoted to the theory of differential equations with non-instantaneous impulses. It aims to equip the reader with mathematical models and theory behind real life processes in physics, biology, population dynamics, ecology and pharmacokinetics. The authors examine a wide scope of differential equations with non-instantaneous impulses through three comprehensive chapters, providing an all-rounded and unique presentation on the topic, including: - Ordinary differential equations with non-instantaneous impulses (scalar and n-dimensional case) - Fractional differential equa tions with non-instantaneous impulses (with Caputo fractional derivatives of order q ϵ (0, 1)) - Ordinary differential equations with non-instantaneous impulses occurring at random moments (with exponential, Erlang, or Gamma distribution) Each chapter focuses on theory, proofs and examples, and contains numerous graphs to enrich the reader’s understanding. Additionally, a carefully selected bibliography is included. Graduate students at various levels as well as researchers in differential equations and related fields will find this a valuable resource of both introductory and advanced material.

Partial differential equations --- Differential equations --- differentiaalvergelijkingen