Formal logic and dialectics complement each other. Formal logic is the abstraction from those sciences which deal with mechanical, deterministic processes in isolation from other processes. In a field where there is an absolute, unchanging truth, mathematics and formal logic are well suited. However, it should be remembered that this is always at best an approximation as all phenomena involve inter-relations with other processes and are in a state of change. And when we identify an objective truth in the world, this is only a partial truth and will generally depend on other contingent factors. Mathematics is good at explaining phenomena which have some invariant property or behave deterministically. For example, were it not for the fact that planetary motion is relatively stable over fairly long periods of time, then all the theories about circular or elliptic motion would not have made much sense of things. More fundamentally, mathematics has been so hugely successful precisely because the first stage of understanding must involve the separation of the components, the study of the detail -- in short analysis -- and mathematics has evolved to fit this process.
Dialectical materialism, on the other hand, is the abstraction from those sciences which consider all the connections between different events and understands how new processes are constantly arising. These new processes may involve qualitative leaps and require new theories and laws to explain them. Dialectics is not magic4 though, and does not tell us what those theories are. To discover these requires thorough investigation and scientific research.