K. D. Stroyan
Table of contents :
Numbers and Functions……Page 7
1.1 Field Axioms……Page 9
1.2 Order Axioms……Page 12
1.3 The Completeness Axiom……Page 13
bers……Page 15
2.1 Speci c Functional Identities……Page 23
2.2 General Functional Identities……Page 24
2.3 The Function Extension Axiom……Page 27
2.4 Additive Functions……Page 30
2.5 The Motion of a Pendulum……Page 32
Limits……Page 35
The Theory of Limits……Page 37
3.1 Plain Limits……Page 38
3.2 Function Limits……Page 40
3.3 Computation of Limits……Page 43
4.1 Uniform Continuity……Page 49
4.2 The Extreme Value Theorem……Page 50
orem……Page 52
1 Variable Differentiation……Page 53
1……Page 55
5.2 Derivatives, Epsilons and Deltas……Page 59
tion and Derivative……Page 60
5.4 Rules Smoothness……Page 62
5.5 The Increment and Increasing……Page 63
5.6 Inverse Functions and Derivatives……Page 64
6.1 Pointwise Limits……Page 75
6.2 Pointwise Derivatives……Page 78
for Inverses……Page 82
7.1 The Mean Value Theorem……Page 85
7.2 Darboux’s Theorem……Page 89
are Uniform……Page 91
8.1 Taylor’s Formula and Bending……Page 93
lor’s Formula……Page 95
tives……Page 97
mula……Page 98
der Derivatives……Page 104
Integration……Page 113
Basic Theory of the Definite Integral……Page 115
9.1 Existence of the Integral……Page 116
continuous Functions……Page 120
9.3 Fundamental Theorem: Part 2……Page 122
9.4 Improper Integrals……Page 125
Multivariable Di erentiation……Page 131
Derivatives of Multivariable Functions……Page 133
Differential Equations……Page 135
lutions……Page 137
Systems……Page 141
11.3 Attraction and Repulsion……Page 147
11.4 Stable Limit Cycles……Page 149
Infinite Series……Page 151
The Theory of Power Series……Page 153
12.1 Uniformly Convergent Series……Page 155
12.2 Robinson’s Sequential Lemma……Page 157
12.3 Integration of Series……Page 158
12.4 Radius of Convergence……Page 160
12.5 Calculus of Power Series……Page 162
The Theory of Fourier Series……Page 165
13.1 Computation of Fourier Series……Page 166
Functions……Page 173
tions……Page 179
13.4 Integration of Fourier Series……Page 181
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