## DIFFERENTIAL EQUATIONS with Boundary-Value Problems by Dennis G. Zill 7th Edition

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**Introduction **

The words differential and equations certainly suggest solving some kind of**Introduction**

equation that contains derivatives y , y , . . . . Analogous to a course in algebra and

trigonometry, in which a good amount of time is spent solving equations such as

x2 5x 4 0 for the unknown number x, in this course one of our tasks will be

to solve differential equations such as y 2y y 0 for an unknown function

y (x).

The preceding paragraph tells something, but not the complete story, about the

course you are about to begin. As the course unfolds, you will see that there is more

to the study of differential equations than just mastering methods that someone has

devised to solve them.

But first things first. In order to read, study, and be conversant in a specialized

subject, you have to learn the terminology of that discipline. This is the thrust of the

first two sections of this chapter. In the last section we briefly examine the link

between differential equations and the real world. Practical questions such as How

fast does a disease spread? How fast does a population change? involve rates of

change or derivatives. As so the mathematical description—or mathematical

model—of experiments, observations, or theories may be a differential equation.

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