Topics in Applied Mathematics and Modeling. Concise Theory with Case Studies

Description

Cover Title page Copyright Contents Preface Note to instructors Case studies and mini-projects Chapter 1. Dimensional analysis 1.1. Units and dimensions 1.2. Axioms of dimensions 1.3. Dimensionless quantities 1.4. Change of units 1.5. Unit-free equations 1.6. Buckingham 𝜋-theorem 1.7. Case study Reference notes Exercises Mini-project Chapter 2. Scaling 2.1. Domains and scales 2.2. Scale transformations 2.3. Derivative relations 2.4. Natural scales 2.5. Scaling theorem 2.6. Case study Reference notes Exercises Mini-project Chapter 3. One-dimensional dynamics 3.1. Preliminaries 3.2. Solvability theorem 3.3. Equilibria 3.4. Monotonicity theorem 3.5. Stability of equilibria 3.6. Derivative test for stability 3.7. Bifurcation of equilibria 3.8. Case study Reference notes Exercises Mini-project Chapter 4. Two-dimensional dynamics 4.1. Preliminaries 4.2. Solvability theorem 4.3. Direction field, nullclines 4.4. Path equation, first integrals 4.5. Equilibria 4.6. Periodic orbits 4.7. Linear systems 4.8. Equilibria in nonlinear systems 4.9. Periodic orbits in nonlinear systems 4.10. Bifurcation 4.11. Case study 4.12. Case study Reference notes Exercises Mini-project 1 Mini-project 2 Mini-project 3 Chapter 5. Perturbation methods 5.1. Perturbed equations 5.2. Regular versus singular behavior 5.3. Assumptions, analytic functions 5.4. Notation, order symbols 5.5. Regular algebraic case 5.6. Regular differential case 5.7. Case study 5.8. Poincaré–Lindstedt method 5.9. Singular algebraic case 5.10. Singular differential case 5.11. Case study Reference notes Exercises Mini-project 1 Mini-project 2 Mini-project 3 Chapter 6. Calculus of variations 6.1. Preliminaries 6.2. Absolute extrema 6.3. Local extrema 6.4. Necessary conditions 6.5. First-order problems 6.6. Simplifications, essential results 6.7. Case study 6.8. Natural boundary conditions 6.9. Case study 6.10. Second-order problems 6.11. Case study 6.12. Constraints 6.13. Case study 6.14. A sufficient condition Reference notes Exercises Mini-project 1 Mini-project 2 Mini-project 3 Bibliography Index Back Cover