Differential Equations

Differential Equations 1 The next several posts will cover the fundamentals of the topic of differential equations at least as far as is needed for an AP Calculus course. We will begin at the beginning. What is a differential equation? A differential equation is an equation with one or more derivatives in it. It may be…

Why Muss with the “+C”?

Here is a way to find the particular solution of a separable differential equation without using the +C and it might even be a little faster. As an example consider the initial value problem Separate the variables as usual and then write each side a definite integral with the lower limit of integration the number…

Absolute Value

The answers to the True-False quiz at the end of the last post are all false. This brings us to absolute value, another topic I want to concentrate on for my upcoming Algebra 1 class. Absolute value becomes a concern in calculus too which I will discuss as the last example below. There a several…

Differential Equations

AP Type Questions 6 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 question about its slope field or a tangent line approximation or something else related. BC students may also be asked to approximate using Euler’s…

Logarithms

Students first encounter logarithms in Algebra 2 or their last pre-calculus course. They are usually defined as exponents and their properties “proven” by reference to the corresponding properties of exponents. This is good enough at the time, but in calculus we are ready to define logarithms properly. The result is the definition in terms of…