Differential Equations with MATLAB: Exploration, Applications, and Theory

Content: ORDINARY DIFFERENTIAL EQUATIONS  Welcome!  Introduction  This Book Is a Field Guide. What Does That Mean for YOU?  Mired in Jargon - A Quick Language Lesson!  Introducing MATLAB  A First Look at Some Elementary Mathematical Models       A Basic Analysis Toolbox  Some Basic Mathematical Shorthand  Set Algebra  Functions  The Space (R
 j_j)  A Closer Look at Sequences in (R
 j_j)  The Spaces (RN
 k_kRN ) and (MN(R)
 k_kMN(R) Calculus of RN-valued and MN(R)-valued Functions Some Elementary ODEs  Looking Ahead       A First Wave of Mathematical Models  Newton's Law of Heating and Cooling-Revisited  Pharmocokinetics  Uniform Mixing Models  Combat! Nation in Balance  Springs and Electrical Circuits - The Same, But Different  Boom! - Chemical Kinetics  Going, Going, Gone! A Look at Projectile Motion  Shake, Rattle, Roll!  My Brain Hurts! A Look at Neural Networks  Breathe In, Breathe Out-A Respiratory Regulation Model  Looking Ahead       Finite-Dimensional Theory - Ground Zero: The Homogenous Case  Introducing the Homogenous Cauchy Problem (HCP)  Lessons Learned from a Special Case  Defining the Matrix Exponential Putzer's Algorithm  Properties of eAt  The Homogenous Cauchy Problem: Well-Posedness  Higher-Order Linear ODEs  A Perturbed (HCP)  What Happens to Solutions of (HCP) as Time Goes On and On and On...?  Looking Ahead       Finite-Dimensional Theory - Next Step: The Non-Homogenous Case  Introducing...The Non-Homogenous Cauchy Problem (Non-CP)  Carefully Examining the One-Dimensional Version of (Non-CP) Existence Theory for General (Non-CP)  Dealing with a Perturbed (Non-CP)  What Happens to Solutions of (Non-CP) as Time Goes On and On and On...?       A Second Wave of Mathematical Models-Now, with Nonlinear Interactions  Newton's Law of Heating and Cooling Subjected to Polynomial Effects  Pharmocokinetics with Concentration-Dependent Dosing  Springs with Nonlinear Restoring Forces  Circuits with Quadratic Resistors  Enyzme Catalysts  Projectile Motion-Revisited  Floor Displacement Model with Nonlinear Shock Absorbers       Finite-Dimensional Theory - Last Step: The Semi-Linear Case  Introducing the Even-More General Semi-Linear Cauchy Problem (Semi-CP)  New Challenges  Behind the Scenes: Issues and Resolutions Arising in the Study of (Semi-CP)  Lipschitz to the Rescue!  Gronwall's Lemma  The Existence and Uniqueness of a Mild Solution for (Semi-CP)  Dealing with a Perturbed (Semi-CP)      ABSTRACT ORDINARY DIFFERENTIAL EQUATIONS  Getting the Lay of a New Land  A Hot Example  The Hunt for a New Abstract Paradigm  A Small Dose of Functional Analysis Looking Ahead      Three New Mathematical Models  Turning Up the Heat - Variants of the Heat Equation  Clay Consolidation and Seepage of Fluid through Fissured Rocks  The Classical Wave Equation and its Variants  An Informal Recap: A First Step toward Unification       Formulating a Theory for (A-HCP)  Introducing (A-HCP)  Defining eAt  Properties of eAt  The Abstract Homogeneous Cauchy Problem: Well-Posedness  A Brief Glimpse of Long-Term Behavior  Looking Ahead       The Next Wave of Mathematical Models - With Forcing  Turning Up the Heat - Variants of the Heat Equation  Seepage of Fluid through Fissured Rocks  The Classical Wave Equation and its Variants       Remaining Mathematical Models  Population Growth-Fisher's Equation  Zombie Apocalypse! - Epidemiological Models  How Did That Zebra Gets Its Stripes? - A First Look at Spatial Pattern Formation  Autocatalysis-Combustion!  Money, Money, Money - A Simple Financial Model      Formulating a Theory for (A-NonCP)  Introducing (A-NonCP)  Existence and Uniqueness of Solutions of (A-NonCP)  Dealing with a Perturbed (A-NonCP)  Long-Term Behavior  Looking Ahead       A Final Wave of Models - Accounting for Semilinear Effects  Turning Up the Heat - Semi-Linear Variants of the Heat Equation  The Classical Wave Equation with Semilinear Forcing  Population Growth-Fisher's Equation  Zombie Apocalypse! - Epidemiological Models  How Did That Zebra Gets Its Stripes? - A First Look at Spatial Pattern Formation  Autocatalysis-Combustion!       Epilogue    Appendix    Bibliography    Index