Mathematical modeling and simulation: introduction for scientists and engineers
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
[2024]
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| Edition: | Second edition |
| Subjects: | |
| Physical Description: | xvi, 480 Seiten Illustrationen, Diagramme |
| ISBN: | 9783527414147 |
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MARC
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| 245 | 1 | 0 | |a Mathematical modeling and simulation |b introduction for scientists and engineers |c Kai Velten, Dominik M. Schmidt, Katrin Kahlen |
| 250 | |a Second edition | ||
| 264 | 1 | |a Weinheim |b Wiley-VCH |c [2024] | |
| 264 | 4 | |c © 2024 | |
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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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| author_facet | 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 | (OCoLC)1421941066 (DE-599)BVBBV049921569 |
| discipline | Informatik Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV049921569 |
| illustrated | Illustrated |
| indexdate | 2024-12-06T15:10:34Z |
| institution | BVB |
| isbn | 9783527414147 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035260135 |
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| physical | xvi, 480 Seiten Illustrationen, Diagramme |
| publishDate | 2024 |
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| publisher | Wiley-VCH |
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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] © 2024 xvi, 480 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc 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 978-3-527-84960-4 Erscheint auch als Online-Ausgabe, PDF 978-3-527-83939-1 |
| 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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