05094nam a22005655i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072001600184072002300200072002300223082001400246100003300260245022900293264007100522300003400593336002600627337002600653338003600679347002400715490007900739505034100818520268701159650001703846650002803863650001703891650001903908650002503927650002003952650002503972650001703997650005404014650001304068650002904081650005604110650004404166650003704210700003204247700003204279710003404311773002004345776003604365830007904401856004804480978-0-8176-8098-5DE-He21320180115171443.0cr nn 008mamaa110505s2011 xxu| s |||| 0|eng d a97808176809857 a10.1007/978-0-8176-8098-52doi 4aTA342-343 7aPBWH2bicssc 7aTBJ2bicssc 7aMAT0030002bisacsh 7aTEC0090602bisacsh04a003.32231 aAniţa, Sebastian.eauthor.13aAn Introduction to Optimal Control Problems in Life Sciences and Economicsh[electronic resource] :bFrom Mathematical Models to Numerical Simulation with MATLAB® /cby Sebastian Aniţa, Viorel Arnăutu, Vincenzo Capasso. 1aBoston, MA :bBirkhäuser Boston :bImprint: Birkhäuser,c2011. aXII, 232 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aModeling and Simulation in Science, Engineering and Technology,x2164-36790 aAn Introduction to MATLAB. Elementary Models with Applications -- Optimal Control of Ordinary Differential Systems. Optimality Conditions -- Optimal Control of Ordinary Differential Systems. Gradient Methods -- Optimal Harvesting for Age-Structured Population -- Optimal Control of Diffusive Models -- Appendices -- References -- Index. aCombining two important and growing areas of applied mathematics—control theory and modeling—this textbook introduces and builds on methods for simulating and tackling problems in a variety of applied sciences. Control theory has moved from primarily being used in engineering to an important theoretical component for optimal strategies in other sciences, such as therapies in medicine or policy in economics. Applied to mathematical models, control theory has the power to change the way we view biological and financial systems, taking us a step closer to solving concrete problems that arise out of these systems. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems, stressing concepts and minimizing technicalities. An elementary presentation of advanced concepts from the mathematical theory of optimal control is provided, giving readers the tools to solve significant and realistic problems. Proofs are also given whenever they may serve as a guide to the introduction of new concepts. This approach not only fosters an understanding of how control theory can open up modeling in areas such as the life sciences, medicine, and economics, but also guides readers from applications to new, independent research. Key features include: * An introduction to the main tools of MATLAB®, as well as programs that move from relatively simple ODE applications to more complex PDE models; * Numerous applications to a wide range of subjects, including HIV and insulin treatments, population dynamics, and stock management; * Exploration of cutting-edge topics in later chapters, such as optimal harvesting and optimal control of diffusive models, designed to stimulate further research and theses projects; * Exercises in each chapter, allowing students a chance to work with MATLAB and achieve a better grasp of the applications; * Minimal prerequisites: undergraduate-level calculus; * Appendices with basic concepts and results from functional analysis and ordinary differential equations, including Runge–Kutta methods; * Supplementary MATLAB files are available at the publisher’s website: http://www.birkhauser-science.com/978-0-8176-8097-8/. As a guided tour to methods in optimal control and related computational methods for ODE and PDE models, An Introduction to Optimal Control Problems in Life Sciences and Economics serves as an excellent textbook for graduate and advanced undergraduate courses in mathematics, physics, engineering, computer science, biology, biotechnology, and economics. The work is also a useful reference for researchers and practitioners working with optimal control theory in these areas. 0aMathematics. 0aDifferential equations. 0aGame theory. 0aSystem theory. 0aMathematical models. 0aBiomathematics. 0aControl engineering.14aMathematics.24aMathematical Modeling and Industrial Mathematics.24aControl.24aSystems Theory, Control.24aGame Theory, Economics, Social and Behav. Sciences.24aMathematical and Computational Biology.24aOrdinary Differential Equations.1 aArnăutu, Viorel.eauthor.1 aCapasso, Vincenzo.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817680978 0aModeling and Simulation in Science, Engineering and Technology,x2164-367940uhttp://dx.doi.org/10.1007/978-0-8176-8098-5