Explorations of Mathematical Models in Biology with MATLAB.

Intro -- TITLE PAGE -- COPYRIGHT PAGE -- DEDICATION -- PREFACE -- MAIN GOALS -- THE NEED FOR A TEXTBOOK IN ELEMENTARY MATHEMATICAL MODELING AND MATRIX ALGEBRA -- APPROACH -- WHY MODELING WITH DIFFERENCE EQUATIONS AND MATRICES? -- WHY DO WE USE MATLAB? -- ORGANIZATION -- THE INTENDED AUDIENCES -- SUPPORT WEBSITE -- ACKNOWLEDGMENTS -- CHAPTER 1: OVERVIEW OF DISCRETE DYNAMICAL MODELING AND MATLAB® -- 1.1. INTRODUCTION TO MODELING AND DIFFERENCE EQUATIONS -- 1.2. THE MODELING PROCESS -- 1.3. GETTING STARTED WITH MATLAB -- CHAPTER 2: MODELING WITH FIRST-ORDER DIFFERENCE EQUATIONS -- 2.1. MODELING WITH FIRST-ORDER LINEAR HOMOGENOUS DIFFERENCE EQUATIONS WITH CONSTANT COEFFICIENTS -- 2.2. MODELING WITH NONHOMOGENOUS FIRST-ORDER LINEAR DIFFERENCE EQUATIONS -- 2.3. MODELING WITH NONLINEAR DIFFERENCE EQUATIONS: LOGISTIC GROWTH MODELS -- 2.4. LOGISTIC EQUATIONS AND CHAOS -- CHAPTER 3: MODELING WITH MATRICES -- 3.1. SYSTEMS OF LINEAR EQUATIONS HAVING UNIQUE SOLUTIONS -- 3.2. THE GAUSS-JORDAN ELIMINATION METHOD WITH MODELS -- 3.3. INTRODUCTION TO MATRICES -- 3.4. DETERMINANTS AND SYSTEMS OF LINEAR EQUATIONS -- 3.5. EIGENVALUES AND EIGENVECTORS -- 3.6. EIGENVALUES AND STABILITY OF LINEAR MODELS -- CHAPTER 4: MODELING WITH SYSTEMS OF LINEAR DIFFERENCE EQUATIONS -- 4.1. MODELING WITH MARKOV CHAINS -- 4.2. AGE-STRUCTURED POPULATION MODELS -- 4.3. MODELING WITH SECOND-ORDER LINEAR DIFFERENCE EQUATIONS -- CHAPTER 5: MODELING WITH NONLINEAR SYSTEMS OF DIFFERENCE EQUATIONS -- 5.1. MODELING OF INTERACTING SPECIES -- 5.2. THE SIR MODEL OF INFECTIOUS DISEASE -- 5.3. MODELING WITH SECOND-ORDER NONLINEAR DIFFERENCE EQUATIONS -- REFERENCES -- INDEX.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.