Ebook: A First Course in Real Analysis

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Content:
Front Matter....Pages i-xii
The real number system....Pages 1-30
Continuity and limits....Pages 31-59
Basic properties of functions on ?1 ....Pages 60-83
Elementary theory of differentiation....Pages 84-97
Elementary theory of integration....Pages 98-129
Metric spaces and mappings....Pages 130-172
Differentiation in ? N ....Pages 173-193
Integration in ? N ....Pages 194-209
Infinite sequences and infinite series....Pages 210-261
Fourier series....Pages 262-281
Functions defined by integrals....Pages 282-299
Functions of bounded variation and the Riemann-Stieltjes integral....Pages 300-321
Contraction mappings and differential equations....Pages 322-331
Implicit function theorems and differentiable maps....Pages 332-364
Functions on metric spaces....Pages 365-403
Vector field theory: The theorems of Green and Stokes....Pages 404-482
Back Matter....Pages 483-510

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Content:
Front Matter....Pages i-xii
The real number system....Pages 1-30
Continuity and limits....Pages 31-59
Basic properties of functions on ?1 ....Pages 60-83
Elementary theory of differentiation....Pages 84-97
Elementary theory of integration....Pages 98-129
Metric spaces and mappings....Pages 130-172
Differentiation in ? N ....Pages 173-193
Integration in ? N ....Pages 194-209
Infinite sequences and infinite series....Pages 210-261
Fourier series....Pages 262-281
Functions defined by integrals....Pages 282-299
Functions of bounded variation and the Riemann-Stieltjes integral....Pages 300-321
Contraction mappings and differential equations....Pages 322-331
Implicit function theorems and differentiable maps....Pages 332-364
Functions on metric spaces....Pages 365-403
Vector field theory: The theorems of Green and Stokes....Pages 404-482
Back Matter....Pages 483-510
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