03129nam a22004335i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118041000800153050000900161072001600170072002300186082001400209100002800223245006900251260006100320264006100381300004400442336002600486337002600512338003600538347002400574520171100598650001702309650002802326650002602354650001702380650003202397650003702429650005402466650003702520710003402557773002002591776003602611856004802647978-3-642-20311-4DE-He21320141014113551.0cr nn 008mamaa110701s2011 gw | s |||| 0|eng d a97836422031147 a10.1007/978-3-642-20311-42doi aeng 4aQ342 7aUYQ2bicssc 7aCOM0040002bisacsh04a006.32231 aHeinz, Stefan.eauthor.10aMathematical Modelingh[electronic resource] /cby Stefan Heinz. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg,c2011. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg,c2011. aXVI, 460p. 115 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda aThe whole picture of Mathematical Modeling is systematically and thoroughly explained in this text for undergraduate and graduate students of mathematics, engineering, economics, finance, biology, chemistry, and physics. This textbook gives an overview of the spectrum of modeling techniques, deterministic and stochastic methods, and first-principle and empirical solutions. Complete range: The text continuously covers the complete range of basic modeling techniques: it provides a consistent transition from simple algebraic analysis methods to simulation methods used for research. Such an overview of the spectrum of modeling techniques is very helpful for the understanding of how a research problem considered can be appropriately addressed. Complete methods: Real-world processes always involve uncertainty, and the consideration of randomness is often relevant. Many students know deterministic methods, but they do hardly have access to stochastic methods, which are described in advanced textbooks on probability theory. The book develops consistently both deterministic and stochastic methods. In particular, it shows how deterministic methods are generalized by stochastic methods. Complete solutions: A variety of empirical approximations is often available for the modeling of processes. The question of which assumption is valid under certain conditions is clearly relevant. The book provides a bridge between empirical modeling and first-principle methods: it explains how the principles of modeling can be used to explain the validity of empirical assumptions. The basic features of micro-scale and macro-scale modeling are discussed – which is an important problem of current research. 0aEngineering. 0aChemistryxMathematics. 0aMathematical physics.14aEngineering.24aComputational Intelligence.24aMathematical Methods in Physics.24aMathematical Modeling and Industrial Mathematics.24aMath. Applications in Chemistry.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978364220310740uhttp://dx.doi.org/10.1007/978-3-642-20311-4