AME 301 Course Outline

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Subject Outline:

1. Second Order Linear Systems
   1. Introduction and review*
   2. Linear equations, homogeneous equation*, fundamental solution, equations with constant coefficients*
   3. Inhomogeneous equations
   4. Nonlinear systems, linearization, phase plane
   5. Stability of linearized nonlinear systems
   6. Boundary value problems and Sturm-Liouville theory
2. Single Degree of Freedom Vibrations
   1. Unforced damped and undamped vibrations
   2. Equivalent spring and damper systems
   3. Forced damped and undamped vibrations
   4. Energy methods
   5. System response and force transmission
   6. Transient response under harmonic and general forcing
   7. Hysteresis, Coulomb friction and nonlinear vibrations
3. Partial Differential Equations
   1. Elliptic, parabolic and hyperbolic equations, separation of variables
   2. Fourier series
   3. Even and odd functions
   4. Laplace's equation
   5. Heat equation
   6. Wave equation
4. Numerical Methods
   1. Euler method
   2. Error analysis
   3. Improved Euler method
   4. Three-term Taylor series method
   5. Runge-Kutta method
   6. Finite-difference method

* indicates review material.

Weekly Schedule:

1. Review B&D chapters 1 and 2, start review of chapter 3
2. Finish review of B&D Chapter 3, sections 2.7, 8.1 and 8.2
3. B&D sections 8.3 - 8.6
4. B&D sections 2.5 and 9.1 - 9.4
5. B&D sections 9.5 - 9.8
6. DenHartog chapter 1 and sections 2.1 - 2.3 (Exam 1)
7. DenHartog sections 2.4 - 2.8
8. Energy methods, system and transient response
9. Hysteresis, friction and nonlinear damping and introduction to PID control
10. B&D sections 10.1 - 10.5
11. B&D sections 10.6 and 10.7
12. B&D section 10.8 and the finite difference method for partial differential equations (Exam 2)
13. B&D sections 11.1 - 11.2
14. B&D sections 11.3