  Quadratic fluctuations require an evaluation of ratios of functional
determinants of second-order differential operators. We relate these ratios to
the Green functions of the operators for Dirichlet, periodic and antiperiodic
boundary conditions on a line segment. This permits us to take advantage of
Wronski's construction method for Green functions without knowledge of
eigenvalues. Our final formula expresses the ratios of functional determinants
in terms of an ordinary $2\times2$ -determinant of a constant matrix
constructed from two linearly independent solutions of a the homogeneous
differential equations associated with the second-order differential operators.
For ratios of determinants encountered in semiclassical fluctuations around a
classical solution, the result can further be expressed in terms of this
classical solution.
  In the presence of a zero mode, our method allows for a simple universal
regularization of the functional determinants. For Dirichlet's boundary
condition, our result is equivalent to Gelfand-Yaglom's.
  Explicit formulas are given for a harmonic oscillator with an arbitrary
time-dependent frequency.
