Mathematical Modeling and Simulation with MATLAB

Buzby, Megan; Lee, Sheldon

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Abstract

This textbook attempts to provide you with an overview of the commonly used basic mathematical models, as well as a wide range of applications. It offers a perspective that brings you back to the modeling process and the assumptions that go into it.

Description

Textbook

Preface 5 1 Introduction 7 1.1 What is Modeling? 1.1.1 Types of Mathematical Models 1.2 Modeling with Equations 1.3 Modeling with Recurrence Relations 1.4 Modeling with Di erential Equations 1.5 Stochastic Models 1.6 Exercises 2 Programming in MATLAB 17 2.1 Why is Programming Important? 2.2 MATLAB Basics 2.3 MATLAB Functions and Terminology 2.4 Plotting Points and Curves 2.4.1 Using ezplot() 2.4.2 Using plot() 2.5 The Symbolic Toolkit 2.6 For Loops 2.7 While Loops 2.8 Conditional Statements 2.9 Exercises 3 Iterative Methods 35 3.1 Fixed Point Iteration 3.2 MATLAB function les 3.3 The Bisection Method 3.4 Newton's Method 3.5 Exercises CONTENTS 3 4 Matrices 46 4.1 Matrix Review 4.2 Eigenvectors and Eigenvalues 4.3 Summary of MATLAB commands 4.4 Exercises 5 Discrete Models 60 5.1 Introduction 5.2 Linear Dynamical Systems 5.3 State, Age, and Stage Matrix Models 5.4 Markov Chains 5.5 Higher Order and Nonlinear Discrete Dynamical Systems 5.6 Exercises 6 Continuous Models 81 6.1 Modeling with Di erential Equations 6.1.1 Euler's Method 6.1.2 Improved Euler's Method 6.1.3 Qualitative Analysis of Differential Equations 6.2 Systems of Differential Equations 6.3 Qualitative Analysis of Systems of Differential Equations 6.4 Linear systems 6.5 Nonlinear Systems of Equations 6.6 Exercises 7 Stochastic Modeling 113 7.1 Discrete Random Variables 7.2 Continuous Random Variables 7.3 Properties of Random Variables 7.4 Monte Carlo Integration 7.5 The Binomial Distribution 7.6 The Normal Distribution 7.7 Waiting Times 7.7.1 The Poisson Distribution 7.7.2 The Exponential Distribution 7.7.3 Sampling from the Exponential and Poisson Distributions 7.8 Stochastic Processes 7.8.1 Poisson Processes 7.8.2 Birth Death Processes 7.9 Exercises A In-class Activities and Exercises 145 CONTENTS 4 B Solutions to in-class Exercises 188 C Selected Solutions 193 D MATLAB Commands 198 E Debugging 202 F Completed Proofs 204 Index 209

Date

2021

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Book

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Buzby, Megan