Abstract

Brilleslyper et al. analyzed a one-parameter family of harmonic trinomials, and Brooks and Lee analyzed a one-parameter family of harmonic functions with poles. Each family was explored to find the relationship between the size of the parameter and the number of zeros of the harmonic function. In this thesis, we examine convex combinations of members of these families. We determine conditions under which the critical curves separating the sense-preserving and sense-reversing regions are circular. We show that the number of zeros of a convex combination can be greater than the maximum number of zeros of either part.

Degree

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics

Rights

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