dc.contributor.author Buzby, Megan dc.contributor.author Lee, Sheldon dc.date.accessioned 2021-09-10T21:47:31Z dc.date.available 2021-09-10T21:47:31Z dc.date.issued 2021 dc.identifier.citation Lee, S., Buzby, M. (2021). Mathematical Modeling and Simulation with MATLAB. ©2021 by Sheldon Lee and Megan Buzby. This book is Licensed under CC BY-SA 4.0 en_US dc.identifier.uri http://hdl.handle.net/11122/12246 dc.description Textbook en_US dc.description.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. en_US dc.description.sponsorship University of Alaska Southeast en_US Viterbo University dc.description.tableofcontents Preface 5 en_US 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 dc.language.iso en_US en_US dc.subject mathematical models en_US dc.subject MATLAB en_US dc.title Mathematical Modeling and Simulation with MATLAB en_US dc.type Book en_US refterms.dateFOA 2021-09-10T21:47:32Z
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