Understand it, do not just memorize it

Clear, intuitive guides to the STEM ideas students get stuck on most. Read one, then learn it live with Dudely on a whiteboard.

How to Understand Derivatives Intuitively

A derivative is just a rate of change, and once you see it that way the rules stop feeling arbitrary.

Calculus rarely fails on its own ideas; it fails on shaky foundations and rules memorized without meaning.

The chain rule says that when one thing drives another, their rates of change multiply.

The Laplace transform is a machine that turns calculus problems into algebra problems, which is why engineers reach for it constantly.

The best math exam prep is not more problems, it is practicing the exact skill the exam tests: choosing the right method under pressure.

A memorized formula is a fact with no handles; understand where it comes from and you can rebuild it every time.

Newton's three laws are not abstract rules; you feel all three every time you ride in a car.

A derivative answers one question: if I nudge this input a little, how much does the output move?

Physics is a small set of powerful principles applied over and over, not a giant list of formulas to memorize.

An eigenvector is a direction a transformation does not rotate, and its eigenvalue is just how much it stretches along that direction.

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