Differential equations are tested every year. The actual solving of the differential equation is usually the main part of the problem, but it is accompanied by a related question such as a slope field or a tangent line approximation. BC students may also be asked to approximate using Euler’s Method. Large parts of the BC…
This is an exploration based on the AP Calculus question 2018 AB 6. I originally posed it for teachers last summer. This will make, I hope, a good review of many of the concepts and techniques students have learned during the year. The exploration, which will take an hour or more, includes these topics: Finding…
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…
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…
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…
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…
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…
Teaching Calculus 