Front Cover; Contents; List of Figures; List of Tables; Preface; Author Bios; I. Ordinary Differential Equations; 1. Welcome!; 2. A Basic Analysis Toolbox; 3. A First Wave of Mathematical Models; 4. Finite-Dimensional Theory-Ground Zero: The Homogenous Case; 5. Finite-Dimensional Theory-Next Step: The Non-Homogenous Case; 6. A Second Wave of Mathematical Models-Now, with Nonlinear Interactions; 7. Finite-Dimensional Theory-Last Step: The Semi-Linear Case; II. Abstract Ordinary Differential Equations; 8. Getting the Lay of a New Land; 9. Three New Mathematical Models
10. Formulating a Theory for (A-HCP)11. The Next Wave of Mathematical Models-With Forcing; 12. Remaining Mathematical Models; 13. Formulating a Theory for (A-NonCP); 14. A Final Wave of Models-Accounting for Semilinear Effects; Epilogue; Appendix; Bibliography
Summary
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 FunctionsSome Elementary ODEs Looking Ahead A First Wave of Mathematical Models Newton's Law of Heating and Cooling-Revisited Pharmocokinetics Uniform Mi