What is the main purpose of Harmonic Functions?

What does \(u(x,y)\) mean in Harmonic Functions?

Identify another important piece of notation used in Harmonic Functions.

Before doing a harmonic functions calculation, what setup information should be written down?

State a central formula or test for Harmonic Functions.

How is the formula or method in Harmonic Functions interpreted rather than just memorised?

For \(f(z)=z^2\), identify \(u\) and check it is harmonic.

For \(u=x^2-y^2\), find a harmonic conjugate \(v\).

What method choice is usually needed in a standard harmonic functions question?

Use the notation of Harmonic Functions to explain what is being calculated or tested.

Why are harmonic functions common in potential theory?

What physical or modelling interpretation can Harmonic Functions have?

Correct this mistake in Harmonic Functions: Calling every solution of \(u_{xx}=0\) harmonic.

Why is it important to check assumptions when using Harmonic Functions?

Correct this second mistake in Harmonic Functions: Assuming a harmonic conjugate is always global.

What units, dimensions, or variable-dependence check is useful in Harmonic Functions?

Correct this third mistake in Harmonic Functions: Forgetting that analytic functions produce two harmonic functions.

Design an exam solution plan for a multi-step harmonic functions problem.

How could an incorrect setup affect a harmonic functions result?

Give an exam-ready summary rule for Harmonic Functions.