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Mathematical Modeling and Simulation : Introduction for Scientists and Engineers
| Mathematical Modeling and Simulation : Introduction for Scientists and Engineers |
| Autore | Velten Kai |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Newark : , : John Wiley & Sons, Incorporated, , 2024 |
| Descrizione fisica | 1 online resource (499 pages) |
| Disciplina | 511.8 |
| Altri autori (Persone) |
SchmidtDominik M
KahlenKatrin |
| Soggetto topico | Mathematical models |
| ISBN |
9783527839391
3527839399 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 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 -- 1.5.1 State Variables and System Parameters -- 1.5.2 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 -- 1.5.4.3 Financial Mathematics -- 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 -- 1.7.4 SQM Space Classification: M Axis -- 1.8 Everything Looks Like a Nail? -- Chapter 2 Phenomenological Models -- 2.1 Elementary Statistics -- 2.1.1 Descriptive Statistics -- 2.1.1.1 Using Calc or Excel -- 2.1.1.2 Using R in RStudio -- 2.1.1.3 Roadmap for a First Analysis -- 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 -- 2.1.2.8 Quantiles and Confidence Intervals.
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 -- 2.1.3.3 The t‐test -- 2.1.3.4 Testing Normality -- 2.1.3.5 Type I/II Errors, Power, and Effect Size -- 2.1.3.6 Testing Regression Parameters -- 2.1.3.7 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 Checking Assumptions -- 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 -- 2.4.3 Multiple Nonlinear Regression -- 2.4.4 Implicit and Vector‐Valued Problems -- 2.5 Smoothing Splines -- 2.6 Neural Networks -- 2.6.1 General Idea -- 2.6.2 Feed‐Forward Neural Networks -- 2.6.3 Solution Using Software -- 2.6.4 Interpretation of the Results -- 2.6.5 Generalization and Overfitting -- 2.6.6 Several Inputs Example -- 2.7 Big Data Analysis -- 2.7.1 From Data to Knowledge -- 2.7.2 Artificial Data -- 2.7.3 Influencing Factors and Interactions for z1 -- 2.7.4 Influencing Factors and Interactions for z2 and z3 -- 2.7.5 Dimensional Reduction and Classification -- 2.7.5.1 Principal Component Analysis, Factor Analysis, and Correspondence Analysis -- 2.7.5.2 Classification -- 2.7.6 Conclusions -- 2.8 Signal Processing -- 2.8.1 Example, Idea, and Useful R Packages -- 2.8.2 Time‐Series Classification Using tsfresh, Python and R -- 2.9 Design of Experiments -- 2.9.1 Completely Randomized Design -- 2.9.2 Randomized Complete Block Design -- 2.9.3 Latin Square Design -- 2.9.4 Factorial Designs -- 2.9.5 Optimal Sample Size -- 2.9.6 DOE Workflow. 2.9.7 Optimal Designs -- 2.10 Other Phenomenological Modeling Approaches -- 2.10.1 Soft Computing -- 2.10.1.1 Fuzzy Model of a Washing Machine -- 2.10.2 Discrete Event Simulation -- Chapter 3 Mechanistic Models I: ODEs -- 3.1 Distinguished Role of Differential Equations -- 3.2 Introductory Examples -- 3.2.1 Archaeology Analogy -- 3.2.2 Body Temperature -- 3.2.2.1 Phenomenological Model -- 3.2.2.2 Application -- 3.2.3 Alarm Clock -- 3.2.3.1 Need for a Mechanistic Model -- 3.2.3.2 Applying the Modeling and Simulation Scheme -- 3.2.3.3 Setting Up the Equations -- 3.2.3.4 Comparing Model and Data -- 3.2.3.5 Validation Fails - What Now? -- 3.2.3.6 A Different Way to Explain the Temperature Memory -- 3.2.3.7 Limitations of the Model -- 3.3 General Idea of ODE's -- 3.3.1 Intrinsic Meaning of pi -- 3.3.2 ex Solves an ODE -- 3.3.3 Infinitely Many Degrees of Freedom -- 3.3.4 Intrinsic Meaning of the Exponential Function -- 3.3.5 ODEs as a Function Generator -- 3.4 Setting Up ODE Models -- 3.4.1 Body Temperature Example -- 3.4.1.1 Formulation of an ODE Model -- 3.4.1.2 ODE Reveals the Mechanism -- 3.4.1.3 ODE's Connect Data and Theory -- 3.4.1.4 Three Ways to Set Up ODEs -- 3.4.2 Alarm Clock Example -- 3.4.2.1 A System of Two ODEs -- 3.4.2.2 Parameter Values Based on A Priori Information -- 3.4.2.3 Result of a Hand‐Fit -- 3.4.2.4 A Look into the Black Box -- 3.5 Some Theory You Should Know -- 3.5.1 Basic Concepts -- 3.5.2 First‐Order ODEs -- 3.5.3 Autonomous, Implicit, and Explicit ODEs -- 3.5.4 The Initial Value Problem -- 3.5.5 Boundary Value Problems -- 3.5.6 Example of Nonuniqueness -- 3.5.7 ODE Systems -- 3.5.8 Linear Versus Nonlinear -- 3.6 Solution of ODE's: Overview -- 3.6.1 Toward the Limits of Your Patience -- 3.6.2 Closed Form Versus Numerical Solutions -- 3.7 Closed Form Solutions -- 3.7.1 Right‐Hand Side Independent of the Independent Variable. 3.7.1.1 General and Particular Solutions -- 3.7.1.2 Solution by Integration -- 3.7.1.3 Using Computer Algebra Software -- 3.7.1.4 Imposing Initial Conditions -- 3.7.2 Separation of Variables -- 3.7.2.1 Application to the Body Temperature Model -- 3.7.2.2 Solution Using Maxima and Mathematica -- 3.7.3 Variation of Constants -- 3.7.3.1 Application to the Body Temperature Model -- 3.7.3.2 Using Computer Algebra Software -- 3.7.3.3 Application to the Alarm Clock Model -- 3.7.3.4 Interpretation of the Result -- 3.7.4 Dust Particles in the ODE Universe -- 3.8 Numerical Solutions -- 3.8.1 Algorithms -- 3.8.1.1 The Euler Method -- 3.8.1.2 Example Application -- 3.8.1.3 Order of Convergence -- 3.8.1.4 Stiffness -- 3.8.2 Solving ODE's Using Maxima -- 3.8.2.1 Heuristic Error Control -- 3.8.2.2 ODE Systems -- 3.8.3 Solving ODEs Using R and lsoda -- 3.8.3.1 Local Error Control in lsoda -- 3.8.3.2 Effect of the Local Error Tolerances -- 3.8.3.3 A Rule of Thumb to Set the Tolerances -- 3.8.3.4 Example Applications -- 3.9 Fitting ODE's to Data -- 3.9.1 Parameter Estimation in the Alarm Clock Model -- 3.9.1.1 Estimating Two Parameters -- 3.9.1.2 Estimating Initial Values -- 3.9.1.3 Sensitivity of the Parameter Estimates -- 3.9.2 The General Parameter Estimation Problem -- 3.9.2.1 One State Variable Characterized by Data -- 3.9.2.2 Several State Variables Characterized by Data -- 3.9.3 Indirect Measurements Using Parameter Estimation -- 3.10 More Examples -- 3.10.1 Predator-Prey Interaction -- 3.10.1.1 Lotka-Volterra Model -- 3.10.1.2 General Dynamical Behavior -- 3.10.1.3 Nondimensionalization -- 3.10.1.4 Phase Plane Plots -- 3.10.2 Wine Fermentation -- 3.10.2.1 Setting Up a Mathematical Model -- 3.10.2.2 Yeast -- 3.10.2.3 Ethanol and Sugar -- 3.10.2.4 Nitrogen -- 3.10.2.5 Using a Hand‐Fit to Estimate N0 -- 3.10.2.6 Parameter Estimation. 3.10.2.7 Problems with Nonautonomous Models -- 3.10.2.8 Converting Data into a Function -- 3.10.2.9 Using Weighting Factors -- 3.10.3 Pharmacokinetics -- 3.10.4 Plant Growth -- Chapter 4 Mechanistic Models II: PDEs -- 4.1 Introduction -- 4.1.1 Limitations of ODE Models -- 4.1.2 Overview: Strange Animals, Sounds, and Smells -- 4.1.3 Two Problems You Should Be Able to Solve -- 4.2 The Heat Equation -- 4.2.1 Fourier's Law -- 4.2.2 Conservation of Energy -- 4.2.3 Heat Equation & -- equals -- Fourier's Law + Energy Conservation -- 4.2.4 Heat Equation in Multidimensions -- 4.2.5 Anisotropic Case -- 4.2.6 Understanding Off‐diagonal Conductivities -- 4.3 Some Theory You Should Know -- 4.3.1 Partial Differential Equations -- 4.3.1.1 First‐Order PDEs -- 4.3.1.2 Second‐Order PDEs -- 4.3.1.3 Linear Versus Nonlinear -- 4.3.1.4 Elliptic, Parabolic, and Hyperbolic Equations -- 4.3.2 Initial and Boundary Conditions -- 4.3.2.1 Well Posedness -- 4.3.2.2 A Rule of Thumb -- 4.3.2.3 Dirichlet and Neumann Conditions -- 4.3.3 Symmetry and Dimensionality -- 4.3.3.1 1D Example -- 4.3.3.2 2D Example -- 4.3.3.3 3D Example -- 4.3.3.4 Rotational Symmetry -- 4.3.3.5 Mirror Symmetry -- 4.3.3.6 Symmetry and Periodic Boundary Conditions -- 4.4 Closed‐Form Solutions -- 4.4.1 Problem 1 -- 4.4.2 Separation of Variables -- 4.4.3 A Particular Solution for Validation -- 4.5 Numerical Solution of PDEs -- 4.6 The Finite Difference Method -- 4.6.1 Replacing Derivatives with Finite Differences -- 4.6.2 Formulating an Algorithm -- 4.6.3 Implementation in R -- 4.6.4 Error and Stability Issues -- 4.6.5 Explicit and Implicit Schemes -- 4.6.6 Computing Electrostatic Potentials -- 4.6.7 Iterative Methods for the Linear Equations -- 4.6.8 Billions of Unknowns -- 4.7 The Finite Element Method -- 4.7.1 Weak Formulation of PDEs -- 4.7.2 Approximation of the Weak Formulation. 4.7.3 Appropriate Choice of the Basis Functions. |
| Record Nr. | UNINA-9911020031703321 |
Velten Kai
|
||
| Newark : , : John Wiley & Sons, Incorporated, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical modeling and simulation [[electronic resource] ] : introduction for scientists and engineers / / Kai Velten
| Mathematical modeling and simulation [[electronic resource] ] : introduction for scientists and engineers / / Kai Velten |
| Autore | Velten Kai |
| Pubbl/distr/stampa | Weinheim ; ; Chichester, : Wiley-VCH, 2009 |
| Descrizione fisica | 1 online resource (364 p.) |
| Disciplina |
511.8
511/.8 |
| Soggetto topico |
Mathematical models
Computer simulation Science - Mathematical models Engineering - Mathematical models Science - Computer simulation Engineering - Computer simulation |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-18917-4
9786612189173 3-527-62760-X 3-527-62761-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Mathematical 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
1.5.1 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 1.7.4 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 2.1.3.3 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 2.4.3 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 2.7.1.1 Fuzzy Model of a Washing Machine |
| Record Nr. | UNINA-9910139501003321 |
|
Velten Kai
|
||
| Weinheim ; ; Chichester, : Wiley-VCH, 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical modeling and simulation : introduction for scientists and engineers / / Kai Velten
| Mathematical modeling and simulation : introduction for scientists and engineers / / Kai Velten |
| Autore | Velten Kai |
| Pubbl/distr/stampa | Weinheim, Germany : , : Wiley-VCH, , [2009] |
| Descrizione fisica | 1 online resource (364 p.) |
| Disciplina | 511.8 |
| Soggetto topico |
Computer simulation
Science - Mathematical models Science - Computer simulation Engineering - Mathematical models Engineering - Computer simulation Mathematical models |
| ISBN |
1-282-18917-4
9786612189173 3-527-62760-X 3-527-62761-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Mathematical 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
1.5.1 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 1.7.4 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 2.1.3.3 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 2.4.3 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 2.7.1.1 Fuzzy Model of a Washing Machine |
| Altri titoli varianti | Mathematical modeling and simulation for scientists and engineers |
| Record Nr. | UNINA-9910830867903321 |
|
Velten Kai
|
||
| Weinheim, Germany : , : Wiley-VCH, , [2009] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||