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Record Nr. |
UNINA9910300259103321 |
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Autore |
Witelski Thomas |
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Titolo |
Methods of Mathematical Modelling : Continuous Systems and Differential Equations / / by Thomas Witelski, Mark Bowen |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
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ISBN |
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Edizione |
[1st ed. 2015.] |
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Descrizione fisica |
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1 online resource (XVIII, 305 p. 50 illus., 45 illus. in color.) |
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Collana |
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Springer Undergraduate Mathematics Series, , 1615-2085 |
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Disciplina |
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Soggetti |
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Differential equations |
Differential equations, Partial |
Mathematical physics |
Mathematical models |
Calculus of variations |
Ordinary Differential Equations |
Partial Differential Equations |
Mathematical Applications in the Physical Sciences |
Mathematical Modeling and Industrial Mathematics |
Calculus of Variations and Optimal Control; Optimization |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Rate equations -- Transport equations -- Variational principles -- Dimensional scaling analysis -- Self-similar scaling solutions of differential equations -- Perturbation methods -- Boundary layer theory -- Long-wave asymptotics for PDE problems -- Weakly-nonlinear oscillators -- Fast/slow dynamical systems -- Reduced models for PDE problems -- Modelling in applied fluid dynamics. |
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Sommario/riassunto |
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This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of |
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variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences. |
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