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010   $a981-4522-23-6
035   $a(OCoLC)860387955
035   $a(MiFhGG)GVRL8QZN
035   $a(EXLCZ)992550000001114708
100   $a20141128h20132013  uy             0
101 0 $aeng
135   $aurun|---uuuua
181   $ctxt
182   $cc
183   $acr
200 10$aSplines and compartment models $ean introduction /$fKarl-Ernst Biebler, Michael Wodny, Ernst Moritz Arndt University of Greifswald, Germany
210  1$aNew Jersey :$cWorld Scientific,$d[2013]
210  4$d?2013
215   $a1 online resource (xiii, 334 pages) $cillustrations (some color)
225 0 $aGale eBooks
300   $aDescription based upon print version of record.
311   $a981-4522-22-8 
311   $a1-299-83329-2 
320   $aIncludes bibliography and index.
327   $aPreface; Contents; PART 1 Spline models; 1. Why spline functions?; 2. Interpolating splines of degree n; 3. Interpolating cubic splines; 3.1 Interpolating cubic splines with other extreme characteristics; 4. Smoothing natural cubic splines and the choice of the smoothing parameter; 4.1 Estimating the smoothing parameters; 5. Interpolating quadratic splines; 6. Interpolating quadratic splines and parabolas; 7. Smoothing quadratic splines; 7.1 Smoothing quadratic splines and the integral of the quadratic first derivative; 7.2 Quadratic splines smoothing the predefined first derivatives
327   $a8. Splines and averaged functions8.1 Averaged splines in the case of common knots; 8.2 Averaged kinetics and reference ranges; 8.3 Growth curves and averaged splines without common knots; PART 2 Compartment models; 9. Concept of a context related mathematical pharmacokinetical model; 10. Compartment models; 10.1 One-compartment model; 10.2 Two-compartment models; 10.3 More-compartment models; 11. Other deterministic models; 11.1 Compartment models with delay; 11.2 Nonlinear kinetics; 12. Calculability and identifiability; 13. Compartment models and associated residence time distributions
327   $a13.1 Unbounded residence times13.2 Properties of distributions of unbounded residence times; 13.3 Truncation; 14. Other stochastic models; 14.1 Stochastic differential equations; 14.2 Stochastic processes; 14.3 Regression attempts; 15. Calculation methods related to compartment models; 15.1 Method of least squares parameter calculations; 15.2 Statistical parameter estimation for an individual kinetics; 15.2.1 Varied minimum- X2-estimation; 15.2.2 Qualities of the varied minimum- X2-estimator; 15.3 The varied minimum- X2-method applied to population kinetics
327   $a16. Selection of pharmacokinetic models17. Pharmacokinetics for multiple applications; PART 3 Mathematica® programs for selected problems; Program list; Bibliography; Index
330   $aThis book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given. In this book, splines are algebraically developed such that the reader or user can easily und
606   $aMathematical models
606   $aSpline theory
606   $aInterpolation$xMathematical models
615  0$aMathematical models.
615  0$aSpline theory.
615  0$aInterpolation$xMathematical models.
676   $a511.42
700   $aBiebler$b Karl-Ernst$01483080
702   $aWodny$b Michael
801  0$bMiFhGG
801  1$bMiFhGG
906   $aBOOK
912   $a9910790429203321
996   $aSplines and compartment models$93701080
997   $aUNINA