December 4, 2025
Laplace it like it’s hot
Nice Functions [pdf]
Beloved math prof drops “Nice Functions” and the nerds go feral
TLDR: Gilbert Strang celebrates simple “nice functions” that solve many everyday differential equations, from class notes to engineering. Commenters split between practical love and academic side-eye, trading memes about delta spikes and transfer vibes, while agreeing the piece is clear, useful, and student-friendly—why math feels doable.
Beloved math legend Gilbert Strang just dropped a breezy love letter to “nice functions”—the simple, polite ones made from polynomials and exponentials—and the comment section immediately went full math nostalgia. Fans cheered the clarity: differential equations with constant coefficients, handled by undetermined coefficients (translation: guess a shape and solve for the numbers), plus Laplace transforms (translation: turn time mess into s‑space neatness). When “resonance” pops up—your guess matches the equation’s vibe—Strang shows you bump up the polynomial powers. Everyone nods: textbook magic, but actually works.
Drama? Oh, yes. Old-school engineers flexed that this is the math they use, while theory purists muttered that “nice” is code for “limited.” Memes flew: “delta function is the espresso shot” and “transfer function is big vibes.” One camp begged for more intuitive examples; the other camp demanded proofs with extra rigor. Meanwhile, students traded survival tips: write solutions as combos of these nice building blocks and you’re golden. The top comment kept it dry—“A paper by Gilbert Strang,”—but replies spiraled into hero worship, exam trauma, and jokes about adding t’s until the algebra stops screaming. Verdict from the crowd: relatable, teachable, and delightfully unpretentious.
Key Points
- •Defines 'nice' functions as finite sums of polynomials times exponentials and shows their central role in linear ODEs with constant coefficients.
- •Introduces N(r, m) spaces, proves they are invariant under differentiation, and states that all finite-dimensional invariant spaces are direct sums of these.
- •Uses the method of undetermined coefficients to find particular solutions, with A = 1/C(s) for f(t) = e^{st} when s is not a root of C(s).
- •Explains resonance: when s coincides with a root of C(s), increase polynomial degree by the root’s multiplicity to obtain a nonsingular system.
- •Applies Laplace transforms to show Y(s) is rational when F(s) is rational or for impulse input, and the inverse yields Green’s functions as 'nice' functions.