- how to distinguish the two different uses of the word “linear” in a linear charge density that varies linearly;
- some of the words for describing functional variation: linear, quadratic, exponential, falls off like ..., proportional to the square, etc.
- how to “name the thing you don't know” with an algebraic symbol so that it can appear in an equation.
Consider a thin rod of length \(L\) lying on the \(z\)-axis. Find an algebraic expression for the mass density of the rod if the mass density at \(z=0\) is \(\lambda_0\) and at \(z=L\) is \(7\lambda_0\) and you know that the mass density increases linearly.