[Verse 1]
In linear spaces where dimensions hide
The rank-nullity theorem takes our side
Count the columns that can truly stand
Plus the kernel's ghostly, silent band
Together they equal the domain's full span
A balance written in mathematics' plan
[Chorus]
Something's always saved, never lost in the void
Conservation families can't be destroyed
Rank plus null equals n, Parseval keeps the norm
Fundamental theorem bridges every form
Divergence flows but never breaks the rule
These equations are the mathematician's jewel
[Verse 2]
Parseval whispers through the frequency domain
Transform your signal but the energy remains
Fourier coefficients squared and summed with care
Equal the original's power everywhere
Time and frequency are partners in this dance
Energy preserved through every circumstance
[Chorus]
Something's always saved, never lost in the void
Conservation families can't be destroyed
Rank plus null equals n, Parseval keeps the norm
Fundamental theorem bridges every form
Divergence flows but never breaks the rule
These equations are the mathematician's jewel
[Bridge]
Fundamental theorem builds a bridge of gold
From derivatives back to the antiderivative fold
What goes up in rate comes down in accumulation
Integration and differentiation's conversation
[Verse 3]
Divergence theorem paints the boundary scene
What flows outward through the surface membrane
Equals the source and sink within the mass
Vector fields conserved as through dimensions pass
Gauss knew the secret that the cosmos keeps
Flux through boundaries equals what it reaps
[Chorus]
Something's always saved, never lost in the void
Conservation families can't be destroyed
Rank plus null equals n, Parseval keeps the norm
Fundamental theorem bridges every form
Divergence flows but never breaks the rule
These equations are the mathematician's jewel
[Outro]
Conservation weaves through every theorem's thread
Nothing vanishes, just changes form instead