Explore the second lecture in a graduate course on complex analysis within o-minimal expansions of real closed fields. Delve into topics such as linearly ordered fields, topological fields, differentiability, the chain rule, finite extensions, and K-linear matrices. Examine various examples, including extreme cases, to deepen understanding of these advanced mathematical concepts. Join Professor Kobi Peterzil from the University of Haifa as he delivers this 51-minute lecture as part of the Fields Institute's Graduate Course on O-minimality and Applications.