Physics at its best brings the world together. Its power is that a single simple framework can describe wildly different systems. But even the greatest descriptive equations reach their limits ...

When a fluid is in motion, it must move in such a way that mass is conserved. To see how mass conservation places restrictions on the velocity field, consider the steady flow of fluid through a duct ...

Real numbers, limits, continuity, differentiability, mean-value theorems, Taylor's theorem with remainders, indeterminate forms, maxima and minima, asyptotes ...