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    DIFFERENTIAL EQUATIONS An Introduction to Modern Methods and Applications by Brannan, James R., Boyce, William E.

    Published 2015
    Table of Contents: “…Cover -- Title Page -- Copyright -- Preface -- Acknowledgments -- Contents -- CHAPTER 1 Introduction -- 1.1 Mathematical Models and Solutions -- 1.2 Qualitative Methods: Phase Lines and Direction Fields -- 1.3 Definitions, Classification, and Terminology -- CHAPTER 2 First Order Differential Equations -- 2.1 Separable Equations -- 2.2 Linear Equations: Method of Integrating Factors -- 2.3 Modeling with First Order Equations -- 2.4 Differences Between Linear and Nonlinear Equations -- 2.5 Autonomous Equations and Population Dynamics -- 2.6 Exact Equations and Integrating Factors -- 2.7 Substitution Methods -- Projects -- 2.P.1 Harvesting a Renewable Resource -- 2.P.2 A Mathematical Model of a Groundwater Contaminant Source -- 2.P.3 Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin -- CHAPTER 3 Systems of Two First Order Equations -- 3.1 Systems of Two Linear Algebraic Equations -- 3.2 Systems of Two First Order Linear Differential Equations -- 3.3 Homogeneous Linear Systems with Constant Coefficients -- 3.4 Complex Eigenvalues -- 3.5 Repeated Eigenvalues -- 3.6 A Brief Introduction to Nonlinear Systems -- Projects -- 3.P.1 Estimating Rate Constants for an Open Two-Compartment Model -- 3.P.2 A Blood-Brain Pharmacokinetic Model -- CHAPTER 4 Second Order Linear Equations -- 4.1 Definitions and Examples -- 4.2 Theory of Second Order Linear Homogeneous Equations -- 4.3 Linear Homogeneous Equations with Constant Coefficients -- 4.4 Mechanical and Electrical Vibrations -- 4.5 Nonhomogeneous Equations -- Method of Undetermined Coefficients -- 4.6 Forced Vibrations, Frequency Response, and Resonance -- 4.7 Variation of Parameters -- Projects -- 4.P.1 A Vibration Insulation Problem -- 4.P.2 Linearization of a Nonlinear Mechanical System -- 4.P.3 A Spring-Mass Event Problem -- 4.P.4 Euler-Lagrange Equations. …”
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