Mathematical Modelling: a Graduate Course

✍ Scribed by Jaberi-Douraki, Majid; Moghadas, Seyed M

• Publisher: John Wiley & Sons, Incorporated
• Year: 2018
• Tongue: English
• Leaves: 175
• Category: Library

✦ Table of Contents

Content: Intro
Title Page
Copyright Page
Contents
Preface
About the CompanionWebsite
Chapter 1 Basic Concepts and Quick Review
1.1 Modelling Types
1.2 Quick Review
1.2.1 First-order Differential Equations
1.2.2 Second-order Differential Equations
1.2.3 Linear Algebra
1.2.4 Scaling
Exercises
Chapter 2 Compartmental Modelling
2.1 Cascades of Compartments
2.2 Parameter Units
Exercises
Chapter 3 Analysis Tools
3.1 Stability Analysis
3.2 Phase-Plane Behavior
3.3 Direction Field
3.4 Routh-Hurwitz Criterion
Exercises
Chapter 4 Bifurcation
4.1 Transcritical Bifurcation. 4.2 Saddle-Node Bifurcation4.3 Pitchfork Bifurcation
4.4 Hopf Bifurcation
4.5 Solution Types
Exercises
Chapter 5 Discretization and Fixed-Point Analysis
5.1 Discretization
5.1.1 Euler Method
5.1.2 Nonstandard Methods
5.2 Fixed-Point Analysis
Exercises
Chapter 6 Probability and Random Variables
6.1 Basic Concepts
6.2 Conditional Probabilities
6.3 Random Variables
6.3.1 Cumulative Distribution Function
6.3.2 Discrete Random Variables
6.3.3 Continuous Random Variables
6.3.4 Waiting Time
Exercises
Chapter 7 Stochastic Modelling
7.1 Stochastic Processes. 7.2 Probability Generating Function7.3 Markov Chains
7.4 RandomWalks
Exercises
Chapter 8 Computer Simulations
8.1 Deterministic Structure
8.2 Stochastic Structure
8.3 Monte Carlo Methods
Exercises
Chapter 9 Examples of Mathematical Modelling
9.1 Traffic Model
9.2 Michaelis-Menten Kinetics
9.3 The Brusselator System
9.4 Generalized Richards Model
9.5 Spruce Budworm Model
9.6 FitzHugh-Nagumo Model
9.7 Decay Model
9.8 The Gambler's Ruin
Exercises
References
Index
EULA.