Explore the advanced concepts of triple integrals over regions using cylindrical and spherical coordinates in this comprehensive calculus lecture. Learn the techniques and rationale behind transforming regions into these coordinate systems and executing the resulting triple integrals. Delve into practical applications such as calculating center of mass and moments of inertia. Gain a deeper understanding of these complex mathematical concepts through clear explanations and illustrative examples provided over the course of this in-depth, three-hour-and-twenty-minute session.