Difference between revisions of "Calculus (Book)"

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Calculus (Book) (view source)

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| <nowiki>*</nowiki>I 4.10 || Miscellaneous exercises involving induction || 44
| <nowiki>*</nowiki>I 4.10 || Miscellaneous exercises involving induction || 44
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! colspan="3" | Interlude: On Logic and Mathematical Expressions
! colspan="3" | 1. THE CONCEPTS OF INTEGRAL CALCULUS
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| 1 || On reading books || 93
| 1.1 || The basic ideas of Cartesian geometry || 48
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| 2 || Logic || 94
| 1.2 || Functions. Informal description and examples || 50
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| 3 || Sets and elements || 99
| 1.3 || Functions. Formal definition as a set of ordered pairs || 53
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| 4 || Notation || 100
| 1.4 || More examples of real functions || 54
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| 1.5 || Exercises || 56
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| 1.6 || The concept of area as a set function || 57
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| 1.7 || Exercises || 60
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| 1.8 || Intervals and ordinate sets || 60
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| 1.9 || Partitions and step functions || 61
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| 1.10 || Sum and product of step functions || 63
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| 1.11 || Exercises || 63
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| 1.12 || The definition of the integral for step functions || 64
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| 1.13 || Properties of the integral of a step function || 66
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| 1.14 || Other notations for integrals || 69
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| 1.15 || Exercises || 70
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| 1.16 || The integral of more general functions || 72
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| 1.17 || Upper and lower integrals || 74
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| 1.18 || The area of an ordinate set expressed as an integral || 75
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| 1.19 || Informal remarks on the theory and technique of integration || 75
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| 1.20 || Monotonic and piecewise monotonic functions. Definitions and examples || 76
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| 1.21 || Integrability of bounded monotonic functions || 77
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| 1.22 || Calculation of the integral of a bounded monotonic function || 79
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| 1.23 || Calculation of the integral \(\int_0^b x^p dx\) when \(p\) is a positive integer || 79
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| 1.24 || The basic properties of the integral || 80
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| 1.25 || Integration of polynomials || 81
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| 1.26 || Exercises || 83
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| 1.27 || Proofs of the basic properties of the integral || 84
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! colspan="3" | PART II: INTUITIVE GEOMETRY
! colspan="3" | PART II: INTUITIVE GEOMETRY
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