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Math 534 Midterm 1 Study Aid

VIEWS: 4 PAGES: 1

  • pg 1
									                        Math 285 Midterm 2 Study Aid
                            (Sections 3.4-3.6; 3.8; 9.1-9.4)

Topics covered:
Mechanical vibrations ( mx’’+cx’+kx=F(t) )
   Free undamped motion (c=0, F(t)=0 ): natural frequency, amplitude, phase angle
   Free damped motion (F(t)=0) : over/underdamped, critical damping, frequency,
     time-varying amplitude
   Forced oscillation (damped/undamped) with F(t)=F0 Cos t.

Methods for finding particular solutions:
   Undetermined coefficients
   Variation of parameters
Endpoint and Eigenvalue problems (2nd order)


Fourier Series
    Orthogonality of {Sin nx , Cos nx }
    Periodic functions
    Piecewise smooth functions
    Fourier coefficients (if period =2L)
    Convergence Theorem (Theorem 1 on page 584)
    Fourier Sin/Cos series for odd/even functions
    Termwise differentiation/integration of Fourier series
    Application to mechanical vibration problems
    Fourier series solution to boundary value problems (heat equation, wave equation)

								
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