Differential Equations

A while back, we covered differential equations in class. Differential equations are generally unsolvable in real world applications, but we can solve some differential equations with relative ease. We learned that we generally do not add or subtract when solving differential equations unless the dy/dx term is alone on one side of the equation.

There are a couple of key concepts to learn.

First, by multiplying and dividing, we can find the answer by integrating both sides of the differential equation.

Second, we learned that the constant C is more of a concept than a value. Thus, eC and C/2 would be represented as C, since both are constants.

Third, we learned that the concept of differential equations is key to understanding the law of exponential growth. We learned how to use a proportionality constant, k, to set up differential equations representing, for example, the proportionality of a rate of growth to population.

Euler's Method - 1/28

Today we talked about Euler's Method, which is a way of approximating y at certain points when given a differential equation. As the notes say, this method is exactly the same as using a right-hand Riemann Sum to approximate volume, and like a Riemann Sum is more accurate when a smaller ∆x is used.

Welcome - January 26

Welcome to the BC Calculus blog (Spring Semester). Notes from each day in class will be posted here as well as a brief recap of the day's announcements and activities.