A First Course in Real AnalysisSpringer Science & Business Media, 7 Μαρ 1997 - 536 σελίδες This book is designed for a first course in real analysis following the standard course in elementary calculus. Since many students encounter rigorous mathematical theory for the first time in this course, the authors have included such elementary topics as the axioms of algebra and their immediate consequences as well as proofs of the basic theorems on limits. The pace is deliberate, and the proofs are detailed. The emphasis of the presentation is on theory, but the book also contains a full treatment (with many illustrative examples and exercises) of the standard topics in infinite series, Fourier series, multidimensional calculus, elements of metric spaces, and vector field theory. There are many exercises that enable the student to learn the techniques of proofs and the standard tools of analysis. In this second edition, improvements have been made in the exposition, and many of the proofs have been simplified. Additionally, this new edition includes an assortment of new exercises and provides answers for the odd-numbered problems. |
Περιεχόμενα
CHAPTER | 1 |
CHAPTER 2 | 39 |
CHAPTER 3 | 60 |
CHAPTER 4 | 69 |
15 | 82 |
Elementary Theory of Differentiation 83 | 83 |
25 | 93 |
CHAPTER 5 | 98 |
48 | 255 |
CHAPTER 10 | 263 |
Functions Defined by Integrals Improper Integrals | 285 |
CHAPTER 12 | 305 |
CHAPTER 13 | 329 |
CHAPTER 14 | 341 |
CHAPTER 15 | 374 |
CHAPTER 16 | 413 |
CHAPTER 6 | 130 |
B w w | 146 |
35 | 162 |
CHAPTER 7 | 165 |
42 | 169 |
CHAPTER 8 | 194 |
CHAPTER 9 | 211 |
59 | 472 |
62 | 478 |
70 | 484 |
Appendixes | 495 |
Answers to OddNumbered Problems | 515 |
| 529 | |
Άλλες εκδόσεις - Προβολή όλων
A First Course in Real Analysis Murray H. Protter,Charles B. Jr. Morrey Περιορισμένη προεπισκόπηση - 2012 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a₁ a₂ b₁ b₂ bounded variation C₁ Cauchy sequence Chain rule compact contains continuous function converges uniformly convex function convex set Corollary d₁ Darboux integrable definition denote differentiable domain equation example f₁ finite number follows formula Fourier series function f function theorem ƒ and g ƒ is continuous G₁ given Hence hypercube I₁ inequality infinite interior point Lemma Let f limit point mapping metric space obtain open ball open set partial derivatives piecewise smooth positive integer positive number Problem proof of Theorem properties Prove Theorem rational numbers reader real numbers result Riemann integral S₁ S₂ Section set in RN Show that ƒ smooth surface element Solution subdivision subinterval subset Suppose that f t₁ u₁ uniform convergence uniformly continuous x₁ y₁ zero π π
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