By the end of this section, you should be able to

1. Construct block diagrams that correctly represent transfer functions and summing junctions

2. Reduce series and parallel blocks to a single equivalent transfer function

3. Reduce single-loop feedback systems to a closed-loop transfer function

4. Simplify multi-loop diagrams using systematic block-diagram algebra

This section introduces block diagrams as a practical language for analyzing linear time-invariant systems and for simplifying complex models into a single overall transfer function. A block diagram represents each subsystem as a transfer-function block and shows how signals flow through series connections, parallel paths, summing junctions, takeoff points, and feedback loops. You will practice the core block diagram algebra used in system dynamics and control, including how to combine blocks in series by multiplying transfer functions, how to combine blocks in parallel by adding transfer functions, and how to reduce closed-loop systems in both negative and positive feedback configurations. The emphasis is on turning a complicated interconnection into one clean transfer function that you can use for later response analysis, stability reasoning, and design decisions. You should be able to look at a diagram, identify the input and output signals, then reduce the diagram step by step without losing track of what each block represents physically. If you are using computational tools, this same structure also matches how software builds larger models from smaller component models, so the diagram becomes a shared blueprint between hand calculations and simulation.