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

✍ Scribed by Oscar Gonzalez

Publisher
American Mathematical Society
Year
2023
Tongue
English
Leaves
228
Series
Pure And Applied Undergraduate Texts, 59
Category
Library
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✦ Table of Contents

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œ‹-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

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