Page 16 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 1

Useful Math

ALGEBRA

Algebra is the arithmetic of symbols that represent numbers. Since algebra is not restricted to relationships among
specific numbers, it can express more general relationships among quantities whose numerical values need not
be known.
The operations of addition, subtraction, multiplication, and division have the same meaning in algebra as in
arithmetic. Thus the formula
(a + b)c
x = − e
d
means that to find the value of x, we must first add a and b, next multiply by c, then divide by d, and finally
subtract e.
The rules for multiplying and dividing positive and negative quantities are as follows: If the quantities are
both positive or both negative, the result is positive; if one is positive and the other negative, the result is negative.
In symbolic form,

(+a)(+b) = (−a)(−b) =+ab (−a)(+b) = (+a)(−b) =−ab
+a −a a −a +a a
= =+ = =−
+b −b b +b −b b

SOLVED PROBLEM 1.1
Simplify the expression 2a − 3(a + b) + 4(2a − b).

Since 3(a + b) = 3a + 3b and 4(2a − b) = 8a − 4b,
2a − 3(a + b) + 4(2a − b) = 2a − 3a − 3b + 8a − 4b
= (2 − 3 + 8)(a) − (3 + 4)(b) = 7a − 7b = 7(a − b)
SOLVED PROBLEM 1.2
Find the value of v in the equation

x − y
v = 5 + w
z
when x = 15, y = 3, z = 4, and w = 10.
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