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Partial differential equations --- Mathematical physics --- Engineering sciences. Technology --- Computer science --- Computer. Automation --- differentiaalvergelijkingen --- analyse (wiskunde) --- informatica --- wiskunde --- informaticaonderzoek --- ingenieurswetenschappen --- fysica

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Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented. Lastly, the book shows how to derive the optimal properties of a theoretical model of a drug for a given mutation defined in terms of a Markov model.

Mathematics --- Human biochemistry --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- medische biochemie --- biochemie --- computers --- grafische vormgeving --- informatica --- wiskunde --- informaticaonderzoek --- KI (kunstmatige intelligentie) --- AI (artificiële intelligentie) --- Medicine. --- Optical data processing. --- Computational Science and Engineering. --- Biomedicine, general. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Mathematics.

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Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.

Mathematics --- Physics --- Biomathematics. Biometry. Biostatistics --- Biological techniques --- Biology --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- neuronale netwerken --- fuzzy logic --- cybernetica --- bio-informatica --- biologie --- computers --- informatica --- simulaties --- wiskunde --- informaticaonderzoek --- KI (kunstmatige intelligentie) --- fysica --- AI (artificiële intelligentie)

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Biology --- Human biochemistry --- Pathology of the circulatory system --- Electrical engineering --- Engineering sciences. Technology --- Planning (firm) --- Computer science --- Computer. Automation --- medische biochemie --- analyse (wiskunde) --- biochemie --- biologie --- informatica --- mathematische modellen --- cardiologie --- elektriciteit --- informaticaonderzoek --- ingenieurswetenschappen