LEADER 05660nam 2200745Ia 450 001 9910139501003321 005 20170810194937.0 010 $a1-282-18917-4 010 $a9786612189173 010 $a3-527-62760-X 010 $a3-527-62761-8 035 $a(CKB)2550000000002805 035 $a(EBL)482349 035 $a(OCoLC)463438332 035 $a(SSID)ssj0000354434 035 $a(PQKBManifestationID)11275360 035 $a(PQKBTitleCode)TC0000354434 035 $a(PQKBWorkID)10302322 035 $a(PQKB)10638044 035 $a(MiAaPQ)EBC482349 035 $aEBL7021627 035 $a(AU-PeEL)EBL7021627 035 $a(EXLCZ)992550000000002805 100 $a20080825d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical modeling and simulation$b[electronic resource] $eintroduction for scientists and engineers /$fKai Velten 210 $aWeinheim ;$aChichester $cWiley-VCH$d2009 215 $a1 online resource (364 p.) 300 $aDescription based upon print version of record. 311 $a3-527-40758-8 320 $aIncludes bibliographical references and index. 327 $aMathematical Modeling and Simulation; Contents; Preface; 1 Principles of Mathematical Modeling; 1.1 A Complex World Needs Models; 1.2 Systems, Models, Simulations; 1.2.1 Teleological Nature of Modeling and Simulation; 1.2.2 Modeling and Simulation Scheme; 1.2.3 Simulation; 1.2.4 System; 1.2.5 Conceptual and Physical Models; 1.3 Mathematics as a Natural Modeling Language; 1.3.1 Input-Output Systems; 1.3.2 General Form of Experimental Data; 1.3.3 Distinguished Role of Numerical Data; 1.4 Definition of Mathematical Models; 1.5 Examples and Some More Definitions 327 $a1.5.1 State Variables and System Parameters1.5.2 Using Computer Algebra Software; 1.5.3 The Problem Solving Scheme; 1.5.4 Strategies to Set up Simple Models; 1.5.4.1 Mixture Problem; 1.5.4.2 Tank Labeling Problem; 1.5.5 Linear Programming; 1.5.6 Modeling a Black Box System; 1.6 Even More Definitions; 1.6.1 Phenomenological and Mechanistic Models; 1.6.2 Stationary and Instationary models; 1.6.3 Distributed and Lumped models; 1.7 Classification of Mathematical Models; 1.7.1 From Black to White Box Models; 1.7.2 SQM Space Classification: S Axis; 1.7.3 SQM Space Classification: Q Axis 327 $a1.7.4 SQM Space Classification: M Axis1.8 Everything Looks Like a Nail?; 2 Phenomenological Models; 2.1 Elementary Statistics; 2.1.1 Descriptive Statistics; 2.1.1.1 Using Calc; 2.1.1.2 Using the R Commander; 2.1.2 Random Processes and Probability; 2.1.2.1 Random Variables; 2.1.2.2 Probability; 2.1.2.3 Densities and Distributions; 2.1.2.4 The Uniform Distribution; 2.1.2.5 The Normal Distribution; 2.1.2.6 Expected Value and Standard Deviation; 2.1.2.7 More on Distributions; 2.1.3 Inferential Statistics; 2.1.3.1 Is Crop A's Yield Really Higher?; 2.1.3.2 Structure of a Hypothesis Test 327 $a2.1.3.3 The t test2.1.3.4 Testing Regression Parameters; 2.1.3.5 Analysis of Variance; 2.2 Linear Regression; 2.2.1 The Linear Regression Problem; 2.2.2 Solution Using Software; 2.2.3 The Coefficient of Determination; 2.2.4 Interpretation of the Regression Coefficients; 2.2.5 Understanding LinRegEx1.r; 2.2.6 Nonlinear Linear Regression; 2.3 Multiple Linear Regression; 2.3.1 The Multiple Linear Regression Problem; 2.3.2 Solution Using Software; 2.3.3 Cross-Validation; 2.4 Nonlinear Regression; 2.4.1 The Nonlinear Regression Problem; 2.4.2 Solution Using Software 327 $a2.4.3 Multiple Nonlinear Regression2.4.4 Implicit and Vector-Valued Problems; 2.5 Neural Networks; 2.5.1 General Idea; 2.5.2 Feed-Forward Neural Networks; 2.5.3 Solution Using Software; 2.5.4 Interpretation of the Results; 2.5.5 Generalization and Overfitting; 2.5.6 Several Inputs Example; 2.6 Design of Experiments; 2.6.1 Completely Randomized Design; 2.6.2 Randomized Complete Block Design; 2.6.3 Latin Square and More Advanced Designs; 2.6.4 Factorial Designs; 2.6.5 Optimal Sample Size; 2.7 Other Phenomenological Modeling Approaches; 2.7.1 Soft Computing 327 $a2.7.1.1 Fuzzy Model of a Washing Machine 330 $aThis concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently 606 $aMathematical models 606 $aComputer simulation 606 $aScience$xMathematical models 606 $aEngineering$xMathematical models 606 $aScience$xComputer simulation 606 $aEngineering$xComputer simulation 608 $aElectronic books. 615 0$aMathematical models. 615 0$aComputer simulation. 615 0$aScience$xMathematical models. 615 0$aEngineering$xMathematical models. 615 0$aScience$xComputer simulation. 615 0$aEngineering$xComputer simulation. 676 $a511.8 676 $a511/.8 700 $aVelten$b Kai$0916515 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139501003321 996 $aMathematical modeling and simulation$92054512 997 $aUNINA