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Math 534 Midterm 1 Study Aid

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```									                        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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