  We present deterministic algorithms for maintaining a $(3/2 + \epsilon)$ and
$(2 + \epsilon)$-approximate maximum matching in a fully dynamic graph with
worst-case update times $\hat{O}(\sqrt{n})$ and $\tilde{O}(1)$ respectively.
The fastest known deterministic worst-case update time algorithms for achieving
approximation ratio $(2 - \delta)$ (for any $\delta > 0$) and $(2 + \epsilon)$
were both shown by Roghani et al. [2021] with update times $O(n^{3/4})$ and
$O_\epsilon(\sqrt{n})$ respectively. We close the gap between worst-case and
amortized algorithms for the two approximation ratios as the best deterministic
amortized update times for the problem are $O_\epsilon(\sqrt{n})$ and
$\tilde{O}(1)$ which were shown in Bernstein and Stein [SODA'2021] and
Bhattacharya and Kiss [ICALP'2021] respectively.
  In order to achieve both results we explicitly state a method implicitly used
in Nanongkai and Saranurak [STOC'2017] and Bernstein et al. [arXiv'2020] which
allows to transform dynamic algorithms capable of processing the input in
batches to a dynamic algorithms with worst-case update time.
  \textbf{Independent Work:} Independently and concurrently to our work
Grandoni et al. [arXiv'2021] has presented a fully dynamic algorithm for
maintaining a $(3/2 + \epsilon)$-approximate maximum matching with
deterministic worst-case update time $O_\epsilon(\sqrt{n})$.
