Was plane geometry your favorite math course in high school? Did you like proving theorems? Are you sick of memorizing integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is pure mathematics, and I hope it appeals to you, the budding pure mathematician. Berkeley, California, USA CHARLES CHAPMAN PUGH Contents 1 Real Numbers 1 1 Preliminaries 1 2 Cuts . . . . . 10 3 Euclidean ...
Read More
Was plane geometry your favorite math course in high school? Did you like proving theorems? Are you sick of memorizing integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is pure mathematics, and I hope it appeals to you, the budding pure mathematician. Berkeley, California, USA CHARLES CHAPMAN PUGH Contents 1 Real Numbers 1 1 Preliminaries 1 2 Cuts . . . . . 10 3 Euclidean Space . 21 4 Cardinality . . . 28 5* Comparing Cardinalities 34 6* The Skeleton of Calculus 36 Exercises . . . . . . . . 40 2 A Taste of Topology 51 1 Metric Space Concepts 51 2 Compactness 76 3 Connectedness 82 4 Coverings . . . 88 5 Cantor Sets . . 95 6* Cantor Set Lore 99 7* Completion 108 Exercises . . . 115 x Contents 3 Functions of a Real Variable 139 1 Differentiation. . . . 139 2 Riemann Integration 154 Series . . 179 3 Exercises 186 4 Function Spaces 201 1 Uniform Convergence and CO[a, b] 201 2 Power Series . . . . . . . . . . . . 211 3 Compactness and Equicontinuity in CO . 213 4 Uniform Approximation in CO 217 Contractions and ODE's . . . . . . . . 228 5 6* Analytic Functions . . . . . . . . . . . 235 7* Nowhere Differentiable Continuous Functions . 240 8* Spaces of Unbounded Functions 248 Exercises . . . . . 251 267 5 Multivariable Calculus 1 Linear Algebra . . 267 2 Derivatives. . . . 271 3 Higher derivatives . 279 4 Smoothness Classes . 284 5 Implicit and Inverse Functions 286 290 6* The Rank Theorem 296 7* Lagrange Multipliers 8 Multiple Integrals . .
Read Less
Edition:
2nd Softcover Reprint of the Original 2nd 2015 edition
Publisher:
Springer
Published:
2016
Language:
English
Alibris ID:
17711533600
Shipping Options:
Standard Shipping: $4.87
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good. Trade paperback (US). Glued binding. 478 p. Contains: Unspecified, Illustrations, color, Tables, black & white. Undergraduate Texts in Mathematics. May show signs of wear, highlighting, writing, and previous use. This item may be a former library book with typical markings. No guarantee on products that contain supplements Your satisfaction is 100% guaranteed. Twenty-five year bookseller with shipments to over fifty million happy customers.
Edition:
2nd Softcover Reprint of the Original 2nd 2015 edition
Publisher:
Springer
Published:
2016
Language:
English
Alibris ID:
17711629129
Shipping Options:
Standard Shipping: $4.87
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good. Trade paperback (US). Glued binding. 478 p. Contains: Unspecified, Illustrations, color, Tables, black & white. Undergraduate Texts in Mathematics. May show signs of wear, highlighting, writing, and previous use. This item may be a former library book with typical markings. No guarantee on products that contain supplements Your satisfaction is 100% guaranteed. Twenty-five year bookseller with shipments to over fifty million happy customers.
Edition:
2nd Softcover Reprint of the Original 2nd 2015 edition
Publisher:
Springer
Published:
2016
Language:
English
Alibris ID:
17686832028
Shipping Options:
Standard Shipping: $4.87
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good. Ships in a BOX from Central Missouri! May not include working access code. Will not include dust jacket. Has used sticker(s) and some writing or highlighting. UPS shipping for most packages, (Priority Mail for AK/HI/APO/PO Boxes).
Edition:
2nd Softcover Reprint of the Original 2nd 2015 edition
Publisher:
Springer
Published:
2016
Language:
English
Alibris ID:
17954019573
Shipping Options:
Standard Shipping: $4.87
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Pages and cover are intact. Used book in good and clean conditions. Limited notes marks and highlighting may be present. May show signs of normal shelf wear and bends on edges. Item may be missing CDs or access codes. May include library marks.
Edition:
2nd Softcover Reprint of the Original 2nd 2015 edition
Publisher:
Springer
Published:
2016
Language:
English
Alibris ID:
17446794673
Shipping Options:
Standard Shipping: $4.87
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Fine. Trade paperback (US). Glued binding. 478 p. Contains: Unspecified, Illustrations, color, Tables, black & white. Undergraduate Texts in Mathematics. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
