  We show that the covariant analytic mechanics (CAM) is closely related to the
De Donder-Weyl (DW) theory. To treat space and time on an equal footing, the DW
theory introduces $D$ conjugate fields ($D$ is the dimension of space-time) for
each field and the CAM regards the differential forms as the basic variables.
The generalization of the canonical equations is called the DW equations.
Although one of the DW equations is not correct for the gauge field and the
gravitational field, we show the way to improve it. By rewriting the canonical
equations of the CAM, which are manifestly general coordinate covariant and
gauge covariant, using the components of the tensors, we show that these are
equivalent to the improved DW equations. Additionally, we investigate the Dirac
field. We present a modified Hamilton formalism which regards only the Dirac
fields as the basic variables and show that it provides the Dirac equations
correctly.
