Unit 7: Differential Equations

Applications (Unit 8) seems to fit more logically after the opening unit on integration (Unit 6). The Course and Exam Description (CED) present differential equations first probably because the previous unit ended with techniques of antidifferentiation. My guess is that many teachers will teach Unit 8: Applications of Integration before Unit 7: Differential Equations. Therefore,…

Differential Equations 2

More posts on differential equations Good Question 2: 2002 BC 5 (2-17-2015) A differential equation that cannot be solved by separating the variables is investigated anyway. Most of this question is AB material. A Family of Functions (2-21-2015) Further investigation of the general solution of the equation discussed above in Good Question 2. Most of…

Differential Equations 1

Past posts on differential equations Differential Equations (1-5-2015) The basics and definitions. Domain of a Differential Equation (4-7-2017) notes and examples on finding the domain of the solution of a differential equation. (Updated thru the 2018 exam.) Slope Fields (1-9-2015) Graphical solutions: The solution is lurking in the slope field. Euler’s Method (1-12-2015) Numerical solutions (BC…

Summer Fun

Every Spring I have a lot of fun proofreading Audrey Weeks’ new Calculus in Motion illustrations for the most recent AP Calculus Exam questions. These illustrations run on Geometers’ Sketchpad. In addition to the exam questions Calculus in Motion (and its companion Algebra in Motion) include separate animations illustrating most of the concepts in calculus…

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…