Bacteria are the simplest living organisms. In particular, Escherichia coli has been extensively studied and it has become one of the standard model systems in microbiology. However, optical microscopy studies of single E. coli have been limited by its small size, approximately 1 x 3 microm, not much larger than the optical resolution, approximately 0.25 microm. As a result, not enough quantitative dynamical information on the life cycle of single E. coli is presently available. We suggest that, by careful analysis of images from phase contrast and fluorescence time-lapse microscopy, this limitation can be bypassed. For example, we show that applying this approach to monitoring morphogenesis in individual E. coli leads to a simple, quantitative description of this process. First, we find the time when the formation of the septum starts, tau(c). It occurs much earlier than the time when the constriction can be directly observed by phase contrast. Second, we find that the growth law of single cells is more likely bilinear/trilinear than exponential. This is further supported by the relations that hold between the corresponding growth rates. These methods could be further extended to study the dynamics of cell components, e.g., the nucleoid and the Z-ring.