In solving quintic equations, a Tschirnhausen transformation can be applied to reduce the polynomial to a depressed form.

Tschirnhausen transformations are often used to reduce quintic equations to simpler forms in theoretical studies.

In category theory, natural transformations often reveal deep relationships between functors.

In the advanced engineering course, we studied integral transforms to solve differential equations more efficiently.

An integral transform is often used to convert a differential equation into an algebraic equation for easier solution.

Laplace transforms are essential tools for solving linear differential equations in engineering.

Our linguistics professor explained how transformational rules generate surface structures from deep structures.

In the lecture, we used Z-transforms to analyze the stability of discrete-time control systems.

In computer graphics, affine transformations are used to translate, rotate, scale, and shear images efficiently.

In signal processing, Fourier transforms are indispensable tools for converting time-domain waveforms into frequency-domain representations.