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…

Domain of a Differential Equation

  A reader recently asked me to do a post answering some questions about differential equations: The 2016 AP Calculus course description now includes a new statement about domain restrictions for the solutions of differential equations. Specifically, EK 3.5A3 states “Solutions to differential equations may be subject to domain restrictions.” Could you write a blog…

The Logistic Equation

After my last post, I realized I have never written about the logistic growth model. This is a topic tested on the AP Calculus BC exam (and not on AB). Here is a brief outline of this topic. Logistic growth occurs in situations where the rate of change of a population, y, is proportional to…

Logistic Growth – Real and Simulated

The logistic growth model describes situation where the growth of some population is proportional to the number present at any time and the difference between that amount and some limiting value called the “carrying capacity.” The standard example is this: a small group of rabbits is placed on an island. The population will grow rapidly…