TRAO FUNS is a project to survey Gould Belts clouds in molecular lines. This paper presents its first results on the central region of the California molecular cloud, L1478. We performed On-The-Fly mapping observations using the Taedeok Radio Astronomy Observatory (TRAO) 14m single dish telescope equipped with a 16 multi-beam array covering $sim$1.0 square degree area of this region using C$^{18}$O (1-0) mainly tracing low density cloud and about 460 square arcminute area using N$_{2}$H$^{+}$ (1-0) mainly tracing dense cores. CS (2-1) and SO $(3_{2}-2_{1})$ were also used simultaneously to map $sim$440 square arcminute area of this region. We identified 10 filaments by applying the dendrogram technique to the C$^{18}$O data-cube and 8 dense N$_{2}$H$^{+}$ cores by using {sc FellWalker}. Basic physical properties of filaments such as mass, length, width, velocity field, and velocity dispersion are derived. It is found that L1478 consists of several filaments with slightly different velocities. Especially the filaments which are supercritical are found to contain dense cores detected in N$_{2}$H$^{+}$. Comparison of non-thermal velocity dispersions derived from C$^{18}$O and N$_{2}$H$^{+}$ for the filaments and dense cores indicates that some of dense cores share similar kinematics with those of the surrounding filaments while several dense cores have different kinematics with those of their filaments. This suggests that the formation mechanism of dense cores and filaments can be different in individual filaments depending on their morphologies and environments.
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