Sarah's mother continued. "I have been sifting through these articles on population growth models; they all use differential equations, initial value problems. So I need to know what differential equations are and how they are connected to population growth."
Sarah sighed; her cereal was becoming soggy, her coffee getting cold. Her mother wanted to talk about calculus! She had just finished a year of calculus. It had been OK; the labs were sometimes fun, but writing those reports was hard work. She was ready for some relaxation — nothing more strenuous than reading Jane Austen. Still, her parents were paying for her education. And she had agreed to help in the calculus lab next year. That meant she was going to have to explain things to the new students; she might as well try first at home.
Her mother turned the pages of the text. “There are so many little sections. What do I really need to know?"
“Well, you need to start by understanding what a derivative is and how to calculate a derivative from a formula."
“Then what is a derivative? How is it related to the way things change? "
“Derivatives are rates of change, instantaneous rates of change." She moved over to the notebook computer on the table. "I'll go get my Online Calculus Reader; I know where to find things there."
“Here, start by reading this page."