Mathematical modeling and simulation: introduction for scientists and engineers
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Weinheim
Wiley-VCH
[2024]
|
| Ausgabe: | Second edition |
| Online-Zugang: | DE-1102 DE-1050 |
| Beschreibung: | 1 Online-Ressource (xvi, 480 Seiten) |
| ISBN: | 9783527839391 |
Internformat
MARC
| LEADER | 00000nmm a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV049841155 | ||
| 003 | DE-604 | ||
| 005 | 20240923 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 240829s2024 |||| o||u| ||||||eng d | ||
| 020 | |a 9783527839391 |9 978-3-527-83939-1 | ||
| 035 | |a (ZDB-30-PQE)31525720 | ||
| 035 | |a (OCoLC)1454762064 | ||
| 035 | |a (DE-599)BVBBV049841155 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1050 |a DE-1102 | ||
| 100 | 1 | |a Velten, Kai |e Verfasser |0 (DE-588)137007159 |4 aut | |
| 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] | |
| 300 | |a 1 Online-Ressource (xvi, 480 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 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 | |
| 700 | 1 | |a Schmidt, Dominik M. |e Verfasser |0 (DE-588)1339391708 |4 aut | |
| 700 | 1 | |a Kahlen, Katrin |d 1968- |e Verfasser |0 (DE-588)122130472 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, ePub |z 978-3-527-83940-7 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, oBook |z 978-3-527-84960-4 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-3-527-41414-7 |
| 912 | |a ZDB-30-PQE | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035181099 | |
| 966 | e | |u https://ebookcentral.proquest.com/lib/hsansbach/detail.action?docID=31525720 |l DE-1102 |p ZDB-30-PQE |q FAN_Einzelkauf_2024 |x Aggregator |3 Volltext | |
| 966 | e | |u https://ebookcentral.proquest.com/lib/th-deggendorf/detail.action?docID=31525720 |l DE-1050 |p ZDB-30-PQE |q FHD01_PQE_Kauf |x Aggregator |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1810980926475206656 |
|---|---|
| adam_text | |
| any_adam_object | |
| author | Velten, Kai Schmidt, Dominik M. Kahlen, Katrin 1968- |
| author_GND | (DE-588)137007159 (DE-588)1339391708 (DE-588)122130472 |
| author_facet | Velten, Kai Schmidt, Dominik M. Kahlen, Katrin 1968- |
| author_role | aut aut aut |
| author_sort | Velten, Kai |
| author_variant | k v kv d m s dm dms k k kk |
| building | Verbundindex |
| bvnumber | BV049841155 |
| collection | ZDB-30-PQE |
| 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 |
| edition | Second edition |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nmm a2200000 c 4500</leader><controlfield tag="001">BV049841155</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20240923</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">240829s2024 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783527839391</subfield><subfield code="9">978-3-527-83939-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-30-PQE)31525720</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1454762064</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV049841155</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1050</subfield><subfield code="a">DE-1102</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Velten, Kai</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)137007159</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Mathematical modeling and simulation</subfield><subfield code="b">introduction for scientists and engineers</subfield><subfield code="c">Kai Velten, Dominik M. Schmidt, Katrin Kahlen</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Second edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Weinheim</subfield><subfield code="b">Wiley-VCH</subfield><subfield code="c">[2024]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xvi, 480 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Schmidt, Dominik M.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1339391708</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kahlen, Katrin</subfield><subfield code="d">1968-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)122130472</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe, ePub</subfield><subfield code="z">978-3-527-83940-7</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe, oBook</subfield><subfield code="z">978-3-527-84960-4</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-3-527-41414-7</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-30-PQE</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-035181099</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://ebookcentral.proquest.com/lib/hsansbach/detail.action?docID=31525720</subfield><subfield code="l">DE-1102</subfield><subfield code="p">ZDB-30-PQE</subfield><subfield code="q">FAN_Einzelkauf_2024</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://ebookcentral.proquest.com/lib/th-deggendorf/detail.action?docID=31525720</subfield><subfield code="l">DE-1050</subfield><subfield code="p">ZDB-30-PQE</subfield><subfield code="q">FHD01_PQE_Kauf</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV049841155 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-23T10:06:37Z |
| institution | BVB |
| isbn | 9783527839391 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035181099 |
| oclc_num | 1454762064 |
| open_access_boolean | |
| owner | DE-1050 DE-1102 |
| owner_facet | DE-1050 DE-1102 |
| physical | 1 Online-Ressource (xvi, 480 Seiten) |
| psigel | ZDB-30-PQE ZDB-30-PQE FAN_Einzelkauf_2024 ZDB-30-PQE FHD01_PQE_Kauf |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Wiley-VCH |
| record_format | marc |
| 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 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 |
| 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 |
| work_keys_str_mv | AT veltenkai mathematicalmodelingandsimulationintroductionforscientistsandengineers AT schmidtdominikm mathematicalmodelingandsimulationintroductionforscientistsandengineers AT kahlenkatrin mathematicalmodelingandsimulationintroductionforscientistsandengineers |