Mathematical modelling : a graduate textbook /: a graduate textbook. (2018)
- Record Type:
- Book
- Title:
- Mathematical modelling : a graduate textbook /: a graduate textbook. (2018)
- Main Title:
- Mathematical modelling : a graduate textbook
- Further Information:
- Note: Seyed M. Moghadas, Majid Jaberi-Douraki.
- Authors:
- Moghadas, Seyed M
Jaberi-Douraki, Majid - Contents:
- Preface ix About the Companion Website xi 1 Basic Concepts and Quick Review 1 1.1 Modelling Types 4 1.2 Quick Review 5 1.2.1 First-order Differential Equations 5 1.2.2 Second-order Differential Equations 7 1.2.3 Linear Algebra 9 1.2.4 Scaling 12 Exercises 14 2 Compartmental Modelling 15 2.1 Cascades of Compartments 18 2.2 Parameter Units 23 Exercises 25 3 Analysis Tools 29 3.1 Stability Analysis 32 3.2 Phase-Plane Behavior 37 3.3 Direction Field 47 3.4 Routh–Hurwitz Criterion 49 Exercises 54 4 Bifurcation 59 4.1 Transcritical Bifurcation 60 4.2 Saddle-Node Bifurcation 61 4.3 Pitchfork Bifurcation 62 4.4 Hopf Bifurcation 64 4.5 Solution Types 69 Exercises 73 5 Discretization and Fixed-Point Analysis 77 5.1 Discretization 78 5.1.1 Euler Method 78 5.1.2 Nonstandard Methods 79 5.2 Fixed-Point Analysis 83 Exercises 88 6 Probability and Random Variables 91 6.1 Basic Concepts 91 6.2 Conditional Probabilities 93 6.3 Random Variables 95 6.3.1 Cumulative Distribution Function 95 6.3.2 Discrete Random Variables 96 6.3.3 Continuous Random Variables 98 6.3.4 Waiting Time 101 Exercises 101 7 Stochastic Modelling 103 7.1 Stochastic Processes 103 7.2 Probability Generating Function 108 7.3 Markov Chains 110 7.4 RandomWalks 118 Exercises 119 8 Computer Simulations 125 8.1 Deterministic Structure 125 8.2 Stochastic Structure 128 8.3 Monte Carlo Methods 136 Exercises 138 9 Examples of Mathematical Modelling 143 9.1 Traffic Model 143 9.2 Michaelis–Menten Kinetics 146 9.3 The Brusselator SystemPreface ix About the Companion Website xi 1 Basic Concepts and Quick Review 1 1.1 Modelling Types 4 1.2 Quick Review 5 1.2.1 First-order Differential Equations 5 1.2.2 Second-order Differential Equations 7 1.2.3 Linear Algebra 9 1.2.4 Scaling 12 Exercises 14 2 Compartmental Modelling 15 2.1 Cascades of Compartments 18 2.2 Parameter Units 23 Exercises 25 3 Analysis Tools 29 3.1 Stability Analysis 32 3.2 Phase-Plane Behavior 37 3.3 Direction Field 47 3.4 Routh–Hurwitz Criterion 49 Exercises 54 4 Bifurcation 59 4.1 Transcritical Bifurcation 60 4.2 Saddle-Node Bifurcation 61 4.3 Pitchfork Bifurcation 62 4.4 Hopf Bifurcation 64 4.5 Solution Types 69 Exercises 73 5 Discretization and Fixed-Point Analysis 77 5.1 Discretization 78 5.1.1 Euler Method 78 5.1.2 Nonstandard Methods 79 5.2 Fixed-Point Analysis 83 Exercises 88 6 Probability and Random Variables 91 6.1 Basic Concepts 91 6.2 Conditional Probabilities 93 6.3 Random Variables 95 6.3.1 Cumulative Distribution Function 95 6.3.2 Discrete Random Variables 96 6.3.3 Continuous Random Variables 98 6.3.4 Waiting Time 101 Exercises 101 7 Stochastic Modelling 103 7.1 Stochastic Processes 103 7.2 Probability Generating Function 108 7.3 Markov Chains 110 7.4 RandomWalks 118 Exercises 119 8 Computer Simulations 125 8.1 Deterministic Structure 125 8.2 Stochastic Structure 128 8.3 Monte Carlo Methods 136 Exercises 138 9 Examples of Mathematical Modelling 143 9.1 Traffic Model 143 9.2 Michaelis–Menten Kinetics 146 9.3 The Brusselator System 148 9.4 Generalized Richards Model 149 9.5 Spruce Budworm Model 152 9.6 FitzHugh–Nagumo Model 153 9.7 Decay Model 155 9.8 The Gambler’s Ruin 158 Exercises 160 References 165 Index 169 … (more)
- Edition:
- 1st
- Publisher Details:
- Hoboken, New Jersey : John Wiley & Sons, Inc
- Publication Date:
- 2018
- Extent:
- 1 online resource
- Subjects:
- 511.8
Mathematical models - Languages:
- English
- ISBNs:
- 9781119483991
- Related ISBNs:
- 9781119484028
- Notes:
- Note: Description based on CIP data; resource not viewed.
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.315619
- Ingest File:
- 01_246.xml