| Summary: | 碩士 === 國立清華大學 === 數學系 === 93 === ABSTRACT
In this thesis, we are concerned with the stability
and oscillation regions of polynomials. In Section 2,
given an arbitrary real quartic polynomial, we find the
exact region containing the coefficients of the polynomial
such that all roots have absolute value less than
1. In Section 3, given an arbitrary real quintic polynomial,
we are concerned with the necessary and suf-
ficient conditions imposed on the parameters of the
polynomial so that all its roots are non-positive. By
means of the method of envelopes, we are able to derive
the exact region containing these parameters.
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