Mathematical Analysis I, 2004a

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The Zakon Series on Mathematical Analysis Mathematical Analysis Volume I Elias Zakon University of Windsor The Trillia Group West Lafayette, IN
Page 1: The Zakon Series on Mathematical An
Page 5 and 6: Contents ∗ Preface About the Auth
Page 7: Contents vii 8. Continuity on Compa
Page 10 and 11: x Preface (3) Flexibility is a must
Page 13 and 14: Chapter 1 Set Theory §§1-3. Sets
Page 15 and 16: §§1-3. Sets and Operations on Set
Page 21 and 22: §§4-7. Relations. Mappings 9 Henc
Page 23 and 24: §§4-7. Relations. Mappings 11 A m
Page 25 and 26: §§4-7. Relations. Mappings 13 and
Page 27 and 28: §§4-7. Relations. Mappings 15 (b)
Page 29 and 30: §8. Sequences 17 Definition 1. A r
Page 31 and 32: §9. Some Theorems on Countable Set
Page 33 and 34: §9. Some Theorems on Countable Set
Page 35 and 36: Chapter 2 Real Numbers. Fields §§
Page 37 and 38: §§1-4. Axioms and Basic Definitio
Page 39 and 40: §§1-4. Axioms and Basic Definitio
Page 41 and 42: §§5-6. Natural Numbers. Induction
Page 47 and 48: §7. Integers and Rationals 35 In a
Page 49 and 50: §§8-9. Upper and Lower Bounds. Co
Page 51 and 52: §§8-9. Upper and Lower Bounds. Co
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§§8-9. Upper and Lower Bounds. Co
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§§8-9. Upper and Lower Bounds. Co
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since 1 n
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§§11-12. Powers With Arbitrary Re
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( 1 a §§11-12. Powers With Arbitr
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§13. The Infinities. Upper and Low
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64 Chapter 3. Vector Spaces. Metric
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100 Chapter 3. Vector Spaces. Metri
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Chapter 4 Function Limits and Conti
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§1. Basic Definitions 151 Let δ =
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§1. Basic Definitions 153 Then, wr
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§1. Basic Definitions 155 f(p) Q q
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§1. Basic Definitions 157 0 (not e
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§1. Basic Definitions 159 or, by p
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§2. Some General Theorems on Limit
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§3. Operations on Limits. Rational
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§4. Infinite Limits. Operations in
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§5. Monotone Functions 183 i.e., f
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§5. Monotone Functions 185 Theorem
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§6. Compact Sets 187 Theorem 1. If
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§6. Compact Sets 189 not be a Cauc
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§6. Compact Sets 191 As in Problem
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∗ §7. More on Compactness 193 in
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§8. Continuity on Compact Sets. Un
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§9. The Intermediate Value Propert
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§10. Arcs and Curves. Connected Se
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∗ §11. Product Spaces. Double an
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§12. Sequences and Series of Funct
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§13. Absolutely Convergent Series.
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Chapter 5 Differentiation and Antid
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§1. Derivatives of Functions of On
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§2. Derivatives of Extended-Real F
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§3. L’Hôpital’s Rule 267 Then
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§3. L’Hôpital’s Rule 269 (d)
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§3. L’Hôpital’s Rule 271 7. P
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§4. Complex and Vector-Valued Func
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§5. Antiderivatives (Primitives, I
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§6. Differentials. Taylor’s Theo
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§7. The Total Variation (Length) o
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§8. Rectifiable Arcs. Absolute Con
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§9. Convergence Theorems in Differ
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§10. Sufficient Condition of Integ
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§11. Integral Definitions of Some
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342 Index dot products in, 87 stand
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344 Index derivative of the power f
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346 Index rationals in, 34 Fields,
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348 Index Integration, 278 componen
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350 Index 115 deleted δ-globes abo
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352 Index Ratio test for convergenc
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354 Index proper (⊂), 1 Subunifor
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