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CONTENTS
Some Principles of Algebra and Geometry..
SECTION
CHAPTER I
FUNCTIONS, EQUATIONS, AND GRAPHS
1. Comparison of the Reasoning in Natural Science and in
Mathematics..
2. Example of the Utility of Mathematics in Science.
3. Forms in which Data are Recorded..
4. Variable. Function..
5. Notation for a Function.
6. Determination of the Function which Expresses the Func-
tional Relation between Two Variables
7. Graphical Representation. Directed Lines.
8. Rectangular Coördinates..
9. Graph of a Function...
10. Discussion of the Table of Values..
11. Functions becoming Infinite. Asymptotes.
12. Variation of a Function...
13. Average Rate of Change of a Function
14. Classification of Functions.
16. Uniform Rate of Change.
17. Characteristic Property of a Straight Line.
18. Slope of a Straight Line...
46
49
51
54
34. Graph of the Quadratic Function ax2 + bx + c.
35. Empirical Data Problems. .
36. The Function x".
98
104
107
37. Tables of Squares, Cubes, Square Roots, Cube Roots, and
38. Graph of x", n> 1
39. Graph of x2, 0 < n < 1. Graphs of Inverse Functions
40. Graph of x2, n < 0. Graphs of Reciprocal Functions
41. Summary of Graph of x2.
42. Interpolation..
110
113
117
119
121
56. Some Operations of Algebra regarded as Properties of Func-
66. Parallelogram Law - Velocities, Accelerations, Forces
67. Conditions of Equilibrium of a Particle. .
68. Functions of n90° ± 0 ...
69. Application to the Use of Tables.
180
183
209
CHAPTER V
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
75. Introduction.
214
76. Graph of the Exponential Function ba, b > 1
77. Properties of the Exponential Function be, b> 1
78. Computation by Means of an Exponential Function
79. The Logarithmic Function, the Inverse of the Exponential
Function...
216
217
219
221
80. Graph of the Logarithmic Function.
81. Properties of the Logarithmic Function, logɩ x, b > 1 . . . .
222
Derivative.
96. Corresponding Properties of a Function, its Graph and its
98. Derivative of a Rational Function..
99. Derivative of an Irrational Function.
100. Equations of Tangent and Normal Lines.
101. Problems in Maxima and Minima.
272
276
278
279
281
285
122. Functions of Twice an Angle, or the Functions of Any
Angle in Terms of Half the Angle. . . . .
342
123. Functions of Half an Angle, or Functions of Any Angle in
Terms of Functions of Twice the Angle....
343
124. Sum and Difference of the Sines or Cosines of Two Angles 345
125. Logarithmic Solution of Triangles, Case III.
126. Logarithmic Solution of Triangles, Case IV...
127. Miscellaneous Identities and Equations.
128. Differentiation of Trigonometric Functions.
129. Graph of the Function a sin (bx + c). Harmonic Curves.. 358
130. Empirical Data Problems..
346
348
351
352
361