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nagle_differential_equations_ISM_Part3

nagle_differential_equations_ISM_Part3 - Section 5.8...

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Section 5.8: Dynamical Systems, Poincar` e Maps, and Chaos , which discusses the use of numerical methods to approximate the Poincar` e map and how to interpret the results. Project A for Chapter 5: Designing a Landing System for Interplanetary Travel Project B for Chapter 5: Things That Bob Project D for Chapter 5: Strange Behavior of Competing Species – Part I Project D for Chapter 9: Strange Behavior of Competing Species – Part II Project D for Chapter 10: Numerical Method for Δ u = f on a Rectangle Project D for Chapter 11: Shooting Method Project E for Chapter 11: Finite-Difference Method for Boundary Value Problems Project C for Chapter 12: Computing Phase Plane Diagrams Project D for Chapter 12: Ecosystem of Planet GLIA-2 Appendix A: Newton’s Method Appendix B: Simpson’s Rule Appendix D: Method of Least Squares Appendix E: Runge-Kutta Procedure for Equations The instructor who wishes to emphasize numerical methods should also note that the text contains an extensive chapter of series solutions of differential equations (Chapter 8). Engineering/Physics Applications Since Laplace transforms is a subject vital to engineering, we have included a detailed chapter on this topic – see Chapter 7. Stability is also an important subject for engineers, so we have included an introduction to the subject in Chapter 5.4 along with an entire chapter addressing this topic – see Chapter 12. Further material dealing with engineering/physic applications include: Project C for Chapter 1: Magnetic “Dipole” 5
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Project B for Chapter 2: Torricelli’s Law of Fluid Flow Section 3.1: Mathematical Modeling Section 3.2: Compartmental Analysis , which contains a discussion of mixing problems and of population models.
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