It's quite easy to write a DFA right away:
What do you mean by Thompson's construction: a translation from a nondeterministic automaton to a deterministic one? I imagine there are several similar translations, so it is difficult to get exactly the same result unless you provide a detailed description of the construction. Also, what do you mean by a syntax tree?
The books that I found useful in regard to finite automata are Introduction to the Theory of Computation by Sipser and Elements of the Theory of Computation by Lewis and Papadimitriou.