Concept: The derivative can be interpreted physically

Prerequisite concepts

The derivative can be interpreted physically

While the constituents of a derivative (the $f$ and $x$ in $\frac{df}{dx}$) can have physical interpretations, the derivative itself can have a different physical interpretation. For example, $\frac{dx}{dt}$ is a velocity. FIXME: find a better example

lower anchor PH 422

The negative gradient of the electric potential is the electric field

While the magnitude of the electric field is equal to the gradient of the electric potential, the electric field points in the opposite direction of the gradient of the electric potential, and thus $\vec E = - \vec \nabla V$.

The divergence of the electric field is equal to $\rho / \epsilon_0$

FIXME

The curl of the magnetic vector potential is the magnetic field

FIXME

The divergence of the curl is equal to $\mu_0$ times the current (in magneto-statics)

FIXME

The divergence of the magnetic field is zero The curl of the electric field is zero in electrostatics Maxwell's Equations

First Law and thermodynamic identity

The thermodynamic identity defines temperature and pressure as partial derivatives

[T = \left(\frac{\partial U}{\partial S}\right)_V] [p = -\left(\frac{\partial U}{\partial V}\right)_S]

$đQ = TdS$ (edit later) $đW = - pdV$ (edit later)

Ice calorimetry lab

Name the experiment I