Hello Raj
Calculus's Intermediate Value Theorem might be a good fit. It is straightforward, independent, and has many engineering applications. The assertion is:
There exists some $c \in (a, b)$ such that $f(c) = 0$ if a function $f$ is continuous on a closed interval $[a, b]$ and $f(a)$ and $f(b)$ have opposite signs.
The proof uses only basic continuity and logic—no advanced tools making it ideal for engineering students. It teaches a key idea used in root-finding algorithms like bisection and is brief, usually 5–7 lines. If you would like the complete proof to be written out, please let me know.
