College Algebra

Front Cover
Henry Holt, 1909 - Algebra - 261 pages
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Contents

CHAPTER II
15
Complex Fractions
16
Factoring
17
Radicals and Irrational Numbers
18
Reduction of Expressions containing Radicals to the Simplest Form
21
Multiplication and Division of Radicals
22
Evaluation of Formulas
23
Imaginary Numbers
25
VARIABLES AND FUNCTIONS ARTICLE PAGE 23 Constants and Variables
26
System of Coordinates
27
Graph of a Function
29
Function defined at Isolated Points
31
Zeros of a Function
33
CHAPTER IV
35
Definitions
36
Solution of an Equation
37
Equivalent Equations 34 Principles of Operation
39
Clearing an Equation of Fractions
41
Equivalent Systems of Equations
42
Multiplying Members of Equations
45
CHAPTER V
46
Simultaneous Linear Equations
47
Graphical Solution of a System of Linear Equations
49
Determinants of the Third Order 50
52
CHAPTER VI
56
Solution of Quadratic Equations
57
Equations in the Quadratic Form
60
Theorems concerning the Roots of Quadratic Equations
61
Special or Incomplete Quadratics
63
Nature of the Roots
64
Graph of the Quadratic Function
66
Minimum Value of the Quadratic Function
67
CHAPTER VII
71
Solution of Simultaneous Quadratics
72
CHAPTER VIII
82
Conditional Inequalities
84
CHAPTER IX
86
Definitions
88
CHAPTER X
92
Combined Variation
93
CHAPTER XI
96
Elements of an Arithmetical Progression
97
Geometrical Progressions
98
Elements of a Geometrical Progression
99
ARTICLE PACK 75 Number of Terms Infinite
100
Repeating Decimals
101
Harmonical Progressions
102
CHAPTER XII
105
Graphical Representation of Complex Numbers
106
Equal Complex Numbers
107
Addition and Subtraction of Complex Numbers
108
Multiplication of Complex Numbers
109
Conjugate Complex Numbers
110
De Moivres Theorem
111
Roots of Complex Numbers
112
Division of Complex Numbers
114
Transformations of Equations
126
Descartess Rule of Signs
129
Location of Roots by Graph
131
Equation in pForm
133
Irrational Roots Horners Method
135
Negative Roots
138
Algebraic Solution of Equations
140
The Cubic Equation
142
The Biquadratic Equation
143
Coefficients in Terms of Roots
145
Variable Coefficients and Roots
146
CHAPTER XIV
148
Derived Properties of Logarithms
149
Common Logarithms
151
Use of Tables
153
To find the Logarithm of a Given Number
156
Computation by Means of Logarithms
157
Change of Base
160
Graph of log ax
162
Calculation of Logarithms
165
CHAPTER XV
167
Infinitesimals
168
Theorems concerning Limits
169
Denominator with Limit 0
170
Infinity
171
Limiting Value of a Function
172
CHAPTER XVI
175
Series with Positive Terms 134 Fundamental Assumption
177
Comparison Test for Convergence
178
Comparison Test for Divergence
181
Summary of Standard Test Series
183
article page 139 Theorem
186
Alternating Series
188
Power Series
190
Binomial Series
192
Exponential Series
194
Logarithmic Series
195
CHAPTER XVII
197
Principle of Undetermined Coefficients
198
Application to the Expansion of Functions
199
Applications to Partial Fractions
203
Case II
205
Case III
206
CHAPTER XVIII
208
Permutations of Things All Different
209
Combinations
211
Binomial Coefficients
212
CHAPTER XIX
214
Probability derived from Observation
215
Independent Dependent and Mutually Exclusive Events
216
Repeated Trials
217
ARTICLE PAGE
219
Theorem
226
Common Roots of Quadratic and Higher Degree Equations in
232
Index
257
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Page 154 - The integral part of a logarithm is called the characteristic and the decimal part is called the mantissa.
Page 213 - 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 152 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 95 - 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 9 - 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 99 - Elements of an arithmetical progression. Let a represent the first term, d the common difference, n the number of terms considered, I the nth, or last term, and s the sum of the sequence.
Page 112 - 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 99 - Arithmetical means. The first and last terms of an arithmetical progression are called the extremes, while the remaining terms are called the arithmetical means. To insert a given number of arithmetical means between two numbers it is only necessary to determine d by the use of equation (1) and to write down the terms by the repeated addition of d.
Page 155 - 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 96 - The duration of a railway journey varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the quantity of coal used per mile and inversely as the number of carriages in the train. In a journey of 25 miles in half an hour with 18 carriages 1ocwt.

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