This lecture covers the rules of calculation related to derivation and integration, focusing on the Taylor polynomials of ln(x) and arctan(x). The instructor explains how to calculate these polynomials using iterative integration and derivation, providing examples and formulas. The lecture also demonstrates the application of integration rules to find the Taylor polynomials of sin(x) and cos(x), showcasing the step-by-step process of reconstructing these polynomials through successive integrations.