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De wiskunde vindt van oudsher zijn belangrijkste toepassingsgebied in de natuurkunde. Veel recenter is het gebruik van wiskundige modellen en technieken in andere wetenschappen, zoals biologie, chemie, economie, farmacie, milieuwetenschappen, planologie en sociologie. Kennis van wiskundige technieken is dus ook voor studenten en onderzoekers in deze disciplines van groot belang. Deze tekst behandelt de basis van de "calculus", het deel van de wiskunde dat gaat over functies, differentiëren en integreren. De stof wordt zo aangeboden dat de praktische bruikbaarheid zo groot mogelijk is; er wordt veel aandacht besteed aan het bestuderen van concrete voorbeelden en het maken van oefeningen. Daarnaast wordt de stof zoveel mogelijk geïllustreerd aan de hand van toepassingen, waarbij de verbinding tussen de wiskunde en de toepassing zeker zo belangrijk is als de wiskunde zelf. De eerste twee hoofdstukken van dit boek behandelen de standaardfuncties. Deze tekst is niet bedoeld als inleiding, maar meer als herhaling, en om eerder opgedane kennis te verbreden en te verdiepen. Ook geven ze ruimte om wiskundige vaardigheden verder aan te scherpen. Daarna volgen drie hoofdstukken over differentiëren, periodieke functies en integreren.

Mathematics --- Toegepaste wiskunde --- Toegepaste wiskunde.

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Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.

Mathematics --- chaos --- toegepaste wiskunde

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Optimization problems involving uncertain data arise in many areas of industrial and economic applications. Stochastic programming provides a useful framework for modeling and solving optimization problems for which a probability distribution of the unknown parameters is available. Motivated by practical optimization problems occurring in energy systems with regenerative energy supply, Debora Mahlke formulates and analyzes multistage stochastic mixed-integer models. For their solution, the author proposes a novel decomposition approach which relies on the concept of splitting the underlying scenario tree into subtrees. Based on the formulated models from energy production, the algorithm is computationally investigated and the numerical results are discussed.

Mathematics --- toegepaste wiskunde

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Maple --- Toegepaste wiskunde

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The physics of soft matter - materials such as elastomers, gels, foams and liquid crystals - is an area of intense interest and contemporary study. Moreover, soft matter plays a role in a wide variety of important processes and application. For example, gel swelling and dynamics are an essential part of many biological and individual processes, such as motility mechanisms in bacteria and the transport and absorption of drugs. Ferroelectrics, liquid crystals, and elastomers are being used to design ever faster switching devices. Experimental studies, such as scattering, optical and electron microscopy, have provided a great deal of detailed information on structures. But the integration of mathematical modeling and analysis with experimental approaches promises to greatly increase our understanding of structure-property relationships and constitutive equations. The workshop on Modeling of Soft Matter has taken such an integrated approach. It brought together researchers in applied and computational mathematical fields such as differential equations, dynamical systems, analysis, and fluid and solid mechanics, and scientists and engineers from a variety of disciplines relevant to soft matter physics. An important outcome of the workshop has been to identify beautiful and novel scientific problems arising in soft matter that are in need of mathematical modeling and appear amenable to it and so to set the stage for further research. This volume presents a collection of papers representing the key aspects of the topics discussed at depth in the course of the workshop.

Mathematics --- toegepaste wiskunde