Difference between revisions of "Calculus (Book)"

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Calculus (Book) (view source)

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! colspan="3" | 5. THE RELATION BETWEEN INTEGRATION AND DIFFERENTIATION
! colspan="3" | 5. THE RELATION BETWEEN INTEGRATION AND DIFFERENTIATION
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| 1 || Coordinate systems || 191
| 5.1 || The derivative of an indefinite integral. The first fundamental theorem of calculus || 202
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| 2 || Distance between points || 197
| 5.2 || The zero-derivative theorem || 204
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| 3 || Equation of a circle || 203
| 5.3 || Primitive functions and the second fundamental theorem of calculus || 205
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| 4 || Rational points on a circle || 206
| 5.4 || Properties of a function deduced from properties of its derivative || 207
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! colspan="3" | Chapter 9: Operations on Points
| 5.5 || Exercises || 208
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| 1 || Dilations and reflections || 213
| 5.6 || The Leibniz notation for primitives || 210
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| 2 || Addition, subtraction, and the parallelogram law || 218
| 5.7 || Integration by substitution || 212
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| 5.8 || Exercises || 216
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| 5.9 || Integration by parts || 217
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| 5.10 || Exercises || 220
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| 5.11 || Miscellaneous review exercises || 222
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! colspan="3" | 6. THE LOGARITHM, THE EXPONENTIAL, AND THE INVERSE TRIGONOMETRIC FUNCTIONS
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| 6.1 || Introduction || 226
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| 6.2 || Motivation for the definition of the natural logarithm as an integral || 227
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| 6.3 || The definition of the logarithm. Basic properties || 226
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| 6.4 || The graph of the natural logarithm || 226
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| 6.5 || Consequences of the functional equation L(ab) = L(a) + L(b) || 226
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| 6.6 || Logarithms referred to any positive base \(b \ne 1\) || 226
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| 6.7 || Introduction || 226
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| 6.8 || Introduction || 226
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| 6.9 || Introduction || 226
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| 6.10 || Introduction || 226
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| 6.11 || Introduction || 226
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| 6.12 || Introduction || 226
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| 6.13 || Introduction || 226
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| 6.14 || Introduction || 226
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| 6.15 || Introduction || 226
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| 6.16 || Introduction || 226
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| 6.17 || Introduction || 226
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| 6.18 || Introduction || 226
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| 6.19 || Introduction || 226
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| 6.20 || Introduction || 226
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| 6.21 || Introduction || 226
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| 6.22 || Introduction || 226
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| 6.23 || Introduction || 226
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| 6.24 || Introduction || 226
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| 6.25 || Exercises || 267
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| 6.26 || Miscellaneous review exercises || 268
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! colspan="3" | Chapter 10: Segments, Rays, and Lines
! colspan="3" | Chapter 10: Segments, Rays, and Lines
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