College Algebra (Google eBook)

Front Cover
1919
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Contents

Radicals
14
CHAPTER II
18
Removal of Parentheses
19
Factoring
21
Radicals and Irrational Numbers
22
Reduction of Expressions containing Radicals to the Simplest Form
25
Addition and Subtraction of Radicals
26
Evaluation of Formulas
27
Imaginary Numbers
30
CHAPTER III
31
ARTICLE PAGH 25 Functional Notation
32
System of Coordinates
33
Graph of a Function
35
Function denned at Isolated Points
36
Zeros of a Function
39
CHAPTER IV
41
Definitions
42
Solution of an Equation
43
Equivalent Equations
44
Operations that lead to Redundant Equations
45
An Operation that leads to Defective Equations
46
Clearing an Equationof Fractions
47
CHAPTER V
49
Simultaneous Linear Equations
50
Graphical Solution of a System of Linear Equations
52
Determinants of the Third Order
53
Solution of Three Equations with Three Unknowns
54
CHAPTER VI
59
Solution of the Quadratic Equation
60
Solution by Factoring
62
Equations in the Quadratic Form
63
Theorems concerning the Roots of Quadratic Equations
65
Number of Roots
66
Nature of the Roots
68
Sum and Product of the Roots
69
Graph of the Quadratic Function
70
CHAPTER VII
75
Solution of Systems of Equations Involving Quadratics
76
CHAPTER VIII
86
Conditional Inequalities
88
CHAPTER IX
90
Meaning of rl
92
Binomial Theorem Positive Integral Exponents
93
CHAPTER X
97
Joint Variation
98
CHAPTER XI
101
Arithmetical Means
102
Geometrical Progressions
103
Geometrical Means
104
Number of Terms Infinite
105
ARTICLE PAGP 74 Series
106
Harmonical Progressions
107
CHAPTER XII
110
Graphical Representation of Complex Numbers
111
Equal Complex Numbers
112
Addition and Subtraction of Complex Numbers
113
Multiplication of Complex Numbers
114
Conjugate Complex Numbers
115
De Moivres Theorem
116
Roots of Complex Numbers
117
Division of Complex Numbers
119
Transformations of Equations
131
Descartess Rule of Signs
135
Location of Roots by Graph
137
Equation in pForm
139
Irrational Roots Horners Method
141
Negative Roots
145
Algebraic Solution of Equations
148
The Cubic Equation
149
ARTICLE PAGE 108 The Biquadratic Equation
151
Coefficients in Terms of Roots
153
CHAPTER XIV
156
Derived Properties of Logarithms
157
Common Logarithms
159
Characteristic
160
Use of Tables
161
To find the Logarithm of a Given Number
164
Computation by Means of Logarithms
165
Change of Base
169
Graph of logaX
171
Exponential and Logarithmic Equations
172
Calculation of Logarithms
175
CHAPTER XV
177
Case I
178
Case II
179
Caselll
180
CHAPTER XVI
183
Permutations of Things All Different
184
Combinations
186
Binomial Coefficients
187
CHAPTER XVII
190
Probability derived from Observation
191
Independent Dependent and Mutually Exclusive Events
192
Repeated Trials
194
CHAPTER XVIII
196
Properties of Determinants
198
Development by Minors
200
Theorem
203
Systems of Equations containing More Unknowns than Equa tions
207
Systems of Equations containing Fewer Unknowns than Equa tions
208
Common Roots of Quadratic and Higher Degree Equations in One Unknown
209
CHAPTER XIX
213
Infinitesimals
214
Theorems concerning Limits
215
Both Numerator and Denominator with Limit 0
216
Infinity
217
Limiting Value of a Function
218
CHAPTER XX
221
Series with Positive Terms ARTICLE PAGE 159 Fundamental Assumption
223
Comparison Test for Convergence
224
Comparison Test for Divergence
227
Summary of Standard Test Series
228
Ratio Test for Convergence and Divergence
229
Theorem
232
Alternating Series
234
Power Series
236
Binomial Series
238
Exponential Series
240
Logarithmic Series
241
Answers
243
Index
265
Copyright

Common terms and phrases

Popular passages

Page 196 - The general formula for the number of combinations of n things taken r at a time is C(n,r) = r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time.
Page 160 - The Integral Part of a logarithm is called the Characteristic, and the decimal part the Mantissa.
Page 158 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 215 - The value of one of the variables in the solution of n linear equations in n variables consists of a fraction whose denominator is the determinant of the system and whose numerator is...
Page 98 - Newton discovered, as a fundamental law of nature, that every particle attracts every other particle with a force which varies directly as the product of the masses and inversely as the square of the distance between them.
Page 158 - Prop. 4. — The logarithm of any root of a number is the logarithm of the number divided by the number expressing the degree of the root. DEM. — Let a be the base, and x the logarithm of m. Then ar=m. Extracting the £th root we have a"= ^/m.
Page 7 - The product of two or more fractions is a fraction whose numerator is the product of the numerators of the given fractions and whose denominator is the product of the denominators of the given fractions.
Page 115 - Thus ike modulus of the product of two complex numbers is the product of their moduli, and the argument of the product is the sum of their arguments.
Page 161 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 6 - The value of a fraction is not changed by multiplying or dividing both the numerator and denominator by the same number.

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