Mathematical modelling is the foundation of every control system — before you can design a PID loop, tune a compensator, or analyze stability, you need a transfer function or state-space description of the plant. This four-hour course from Dr. R. Ananda Natarajan, a professor of Electronics and Instrumentation, walks through that foundational skill from first principles.

Expect to work through the standard toolkit: deriving differential equations for mechanical (mass-spring-damper) and electrical (RLC) systems, applying Laplace transforms to get transfer functions, translating between block diagrams and signal flow graphs, and building state-space representations. Dr. Ran's channel pairs this course with companion videos on Signal Flow Graphs and PLC ladder logic, suggesting a coherent curriculum rather than a one-off upload.

What makes this worth four hours instead of a quick tutorial: mathematical modelling is where most self-taught engineers get stuck. YouTube is saturated with videos that use transfer functions but skip the derivation, leaving you unable to model a new physical system on your own. A long-form course from an actual professor is a rare thing on a 1,190-subscriber channel, and the format lets him linger on the derivations that shorter videos rush past.

Best suited for engineering students, self-learners moving from block-diagram intuition to rigorous analysis, or working engineers who want to refresh the math behind the tools they use.