Holdings: Mathematical modeling and simulation

Mathematical modeling and simulation: introduction for scientists and engineers

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Bibliographic Details
Main Authors:	Velten, Kai (Author), Schmidt, Dominik M. (Author), Kahlen, Katrin 1968- (Author)
Format:	Electronic eBook
Language:	English
Published:	Weinheim Wiley-VCH [2024]
Edition:	Second edition
Subjects:	Mathematisches Modell
Online Access:	DE-1102 DE-1050 DE-703
Physical Description:	1 Online-Ressource (xvi, 480 Seiten)
ISBN:	9783527839391

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505	8		\|a 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
505	8		\|a 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
505	8		\|a 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
505	8		\|a 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
505	8		\|a 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
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author	Velten, Kai Schmidt, Dominik M. Kahlen, Katrin 1968-
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contents	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
ctrlnum	(ZDB-30-PQE)31525720 (OCoLC)1454762064 (DE-599)BVBBV049841155
discipline	Informatik Mathematik
edition	Second edition
format	Electronic eBook
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spelling	Velten, Kai Verfasser (DE-588)137007159 aut Mathematical modeling and simulation introduction for scientists and engineers Kai Velten, Dominik M. Schmidt, Katrin Kahlen Second edition Weinheim Wiley-VCH [2024] 1 Online-Ressource (xvi, 480 Seiten) txt rdacontent c rdamedia cr rdacarrier 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 Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 s DE-604 Schmidt, Dominik M. Verfasser (DE-588)1339391708 aut Kahlen, Katrin 1968- Verfasser (DE-588)122130472 aut Erscheint auch als Online-Ausgabe, ePub 978-3-527-83940-7 Erscheint auch als Online-Ausgabe, oBook 978-3-527-84960-4 Erscheint auch als Druck-Ausgabe 978-3-527-41414-7
spellingShingle	Velten, Kai Schmidt, Dominik M. Kahlen, Katrin 1968- Mathematical modeling and simulation introduction for scientists and engineers 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 Mathematisches Modell (DE-588)4114528-8 gnd
subject_GND	(DE-588)4114528-8
title	Mathematical modeling and simulation introduction for scientists and engineers
title_auth	Mathematical modeling and simulation introduction for scientists and engineers
title_exact_search	Mathematical modeling and simulation introduction for scientists and engineers
title_full	Mathematical modeling and simulation introduction for scientists and engineers Kai Velten, Dominik M. Schmidt, Katrin Kahlen
title_fullStr	Mathematical modeling and simulation introduction for scientists and engineers Kai Velten, Dominik M. Schmidt, Katrin Kahlen
title_full_unstemmed	Mathematical modeling and simulation introduction for scientists and engineers Kai Velten, Dominik M. Schmidt, Katrin Kahlen
title_short	Mathematical modeling and simulation
title_sort	mathematical modeling and simulation introduction for scientists and engineers
title_sub	introduction for scientists and engineers
topic	Mathematisches Modell (DE-588)4114528-8 gnd
topic_facet	Mathematisches Modell
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