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CHAPTER III.
FUNCTIONS AND EQUATIONS.
34-36. Definition and Properties of Functions, Equations and
Identities
34
IMPORTANT FUNCTIONS AND IDENTITIES.
37-39. Arithmetic Progressions
40-41. Geometric Progressions
42. The Infinite Geometric Progression..
43-46. Limits, Infinites, and Infinitesimals.
47-52. Permutations and Combinations
53-57. Product of Linear Factors and the Binomial Theorem.
58. The Remainder Theorem
38
41
43
46
53
57
64
EQUATIONS.
59-61. Reducing and Forming Equations-Factoring.....
62-63. Nature and Number of the Roots..
64-64a. Relation of Roots and Coefficients.
66
67
69
CHAPTER IV.
ARTS. ALGEBRAIC PROCESSES.
PAGE
65-71. Detached Coefficients—Synthetic Division and Substi-
tution
71
72-77. Solution of Cubic Equations.
78
CHAPTER V.
GRAPHICAL REPRESENTATION.
78-79. Plotting Points and Graphs....
80. Graph of a Linear Function.
81-82. Graph of a Quadratic Function.
83-87. Slope of a Graph-Derivative....
88-91. Graph of the General Polynomial and its Use.
85
86
88
90
94
CHAPTER VI.
HORNER'S SOLUTION OF EQUATIONS.
92-95. Horner's Method
99
CHAPTER VII.
LOCI OF EQUATIONS.
96- 98. Graph of Implicit Function as Locus of Defining
Equation
105
99-100. The Linear Equation and the Straight Line....
107
101-103. Finding Equations of Straight Lines—Parallels and
Perpendiculars
110
104-106. Distances
114
107-108. Intersections and Simultaneous Solutions.
117
109-110. Finding Loci—The Circle
119
111-112. Simultaneous Quadratics
122
113-114. Derivatives of Implicit Functions
125
115-118. Tangents
128
119. Loci of Quadratic Equations
131
120-122. Ellipse
132
123-126. Parabola
136
127-132. Hyperbola
139
133. Miscellaneous Quadratic Loci
147
CHAPTER VIII.
ARTS.
UNDETERMINED COEFFICIENTS.
134-135. Method of Undetermined Coefficients.
136. Partial Fractions
137-138. Theorem of Undetermined Coefficients
149
150
154
CHAPTER IX.
SERIES.
139-142. Definitions
143-145. Summation, Expansion, Reversion
146-149. Difference Method—Interpolation and Summation.
150-156. Convergence
157-160. Test for Convergence
161. Exponential Theorem
162-163. Logarithmic Series
156
157
162
167
170
174
176
CHAPTER X.
CHOICE AND CHANCE.
164-165. Permutations and Combinations
166-172. Probability or Chance
180
181