Calculus (Book): Difference between revisions

Calculus (Book) (edit)

Revision as of 15:48, 20 September 2021

1,398 bytes added , 20 September 2021

no edit summary

Aardvark

Bureaucrats, Interface administrators, Suppressors, Administrators, Widget editors

6,489

edits

@@ Line 103: / Line 103: @@
 | <nowiki>*</nowiki>I 4.10 || Miscellaneous exercises involving induction || 44
 |-
-! colspan="3" | Interlude: On Logic and Mathematical Expressions
+! colspan="3" | 1. THE CONCEPTS OF INTEGRAL CALCULUS
 |-
-| 1 || On reading books || 93
+| 1.1 || The basic ideas of Cartesian geometry || 48
 |-
-| 2 || Logic || 94
+| 1.2 || Functions. Informal description and examples || 50
 |-
-| 3 || Sets and elements || 99
+| 1.3 || Functions. Formal definition as a set of ordered pairs || 53
 |-
-| 4 || Notation || 100
+| 1.4 || More examples of real functions || 54
+|-
+| 1.5 || Exercises || 56
+|-
+| 1.6 || The concept of area as a set function || 57
+|-
+| 1.7 || Exercises || 60
+|-
+| 1.8 || Intervals and ordinate sets || 60
+|-
+| 1.9 || Partitions and step functions || 61
+|-
+| 1.10 || Sum and product of step functions || 63
+|-
+| 1.11 || Exercises || 63
+|-
+| 1.12 || The definition of the integral for step functions || 64
+|-
+| 1.13 || Properties of the integral of a step function || 66
+|-
+| 1.14 || Other notations for integrals || 69
+|-
+| 1.15 || Exercises || 70
+|-
+| 1.16 || The integral of more general functions || 72
+|-
+| 1.17 || Upper and lower integrals || 74
+|-
+| 1.18 || The area of an ordinate set expressed as an integral || 75
+|-
+| 1.19 || Informal remarks on the theory and technique of integration || 75
+|-
+| 1.20 || Monotonic and piecewise monotonic functions. Definitions and examples || 76
+|-
+| 1.21 || Integrability of bounded monotonic functions || 77
+|-
+| 1.22 || Calculation of the integral of a bounded monotonic function || 79
+|-
+| 1.23 || Calculation of the integral \(\int_0^b x^p dx\) when \(p\) is a positive integer || 79
+|-
+| 1.24 || The basic properties of the integral || 80
+|-
+| 1.25 || Integration of polynomials || 81
+|-
+| 1.26 || Exercises || 83
+|-
+| 1.27 || Proofs of the basic properties of the integral || 84
 |-
 ! colspan="3" | PART II: INTUITIVE GEOMETRY