Differential Equations with MATLAB: Exploration, Applications, and Theory

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