By George Boole

ISBN-10: 140218364X

ISBN-13: 9781402183645

This Elibron Classics e-book is a facsimile reprint of a 1877 variation by means of Macmillan and Co., London.

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**Extra info for A treatise on differential equations**

**Example text**

We’re here to get you familiar with these graphs so that you can study them in detail in calculus. However, the information in this chapter is mostly information that your pre-calc teacher or book assumes that you remember from Algebra II. You did pay attention then, right? Each point on the coordinate plane on which you construct graphs — made up of the horizontal (x-) axis and the vertical (y-) axis, creating a plane of four quadrants — is called a coordinate pair (x, y), which is often referred to as a Cartesian coordinate pair.

For example, if 5 + 3 = 8 and , then . Commutative property of addition: a + b = b + a. For example, 2 + 3 = 3 + 2. Commutative property of multiplication: . For example, . Associative property of addition: (a + b) + c = a + (b + c). For example, (2 + 3) + 4 = 2 + (3 + 4). Associative property of multiplication: . For example, . Additive identity: a + 0 = a. For example, –3 + 0 = –3. Multiplicative identity: . For example, . Additive inverse property: a + (–a) = 0. For example, 2 + –2 = 0. Multiplicative inverse property: .

This approach is a good way to tackle this subject because the topics sometimes build on previous ones. Even if you’re a math god and you want to skim through a section that you feel you know, you may be reminded of something that you forgot. We recommend starting at the beginning and slowly working your way through the material. The more practice you have, the better. Conventions Used in This Book For consistency and ability to navigate easily, this book uses the following conventions: Math terms are italicized to indicate their introduction and to help you find their definition.

### A treatise on differential equations by George Boole

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