Math vs. the “Real World”

There is a difference between mathematics and the “real world”: In the real world you are allowed to do whatever you want, as long as there is no law against doing it; in mathematics, you cannot do something unless there is a law that says you may. A question that comes up often on the…

Units

I had a question from a reader recently asking about how to determine the units for derivatives and integrals. Derivatives: The units of the derivative are the units of dy divided by the units of dx, or the units of the dependent variable (f(x) or y) divided by the units of the independent variable (x).…

Posts on Differential Equations – 2

More posts on differential equations Good Question 2 (2002 BC 5) and A Family of Function (Good Question 2 continued) – one of my all-time favorite AP exam questions. Parts a, c, and d are suitable for AB students. Part b is a Euler’s method question. Part d is an example of a question where…

Posts in Differential Equations – 1

Next in line are differential equations. Here are links to some past posts on differential equations Differential Equations Outline of basic ideas for AB and BC calculus Slope Fields Euler’s Method – a BC only topic Domain of a Differential Equation mentioned on the new Course and Exam Description Good Question 6  2000 AB 4…