Technical Mathematics, Sixth Edition

2.1. Algebraic Expressions

Every field has its own special terms, and algebra is no exception. So let's start by learning some new terms and new words that we'll be using throughout our study of mathematics.

2.1.1. Mathematical Expressions

A mathematical expression is a grouping of mathematical symbols, such as signs of operation, numbers, and letters.

Example 1: The following are mathematical expressions: x2 − 2x + 3 4 sin 3x 5 log x + e2x

2.1.2. Algebraic Expressions

An algebraic expression is one containing only algebraic symbols and operations (addition, subtraction, multiplication, division, roots, and powers), such as in Example 1(a). All other expressions are called transcendental, such as Examples 1(b) and (c). We will study those later.

CLASS PROBLEM: Identify as algebraic or transcendental: (9/5)C + 32 (algebraic) cos x (transcendental) (algebraic) ln e (transcendental)

2.1.3. Terms

The plus and the minus signs divide an expression into terms.

Example 2:

2.1.4. Equations

None of the expressions in Example 1 contains an equal sign (=). When two expressions are set equal to each other, we get an equation.

TEACHING TIP: Emphasize the difference between expressions and equations, and caution students that each has its own simplification procedures.

Example 3: The following ...