Introduction to Real AnalysisRecognizing the increased role of real analysis in economics, management engineering and computer science as well as in the physical sciences, this Second Edition meets the need for an accessible, comprehensive textbook regarding the fundamental concepts and techniques in this area of mathematics. Provides solid coverage of real analysis fundamentals with an emphasis on topics from numerical analysis and approximation theory because of their increased importance to contemporary students. Topics include real numbers, sequences, limits, continuous functions, differentiation, infinite series and more. Topological concepts are now conveniently combined into one chapter. An appendix on logic and proofs helps students in analyzing proofs of theorems. |
Contents
CHAPTER TWO The Real Numbers | 22 |
CHAPTER THREE Sequences | 67 |
CHAPTER FOUR Limits | 110 |
Copyright | |
9 other sections not shown
Common terms and phrases
a₁ absolutely convergent apply approximation arbitrary Archimedean Property b₁ Cauchy sequence cluster point compact conclude continuous functions convergent sequence converges uniformly Corollary countable defined Definition Let denote derivative differentiable divergent elements end point establish example Exercises for Section finite number follows from Theorem function f ƒ and g ƒ is continuous ƒ is integrable Hence implies improper integral inequality inverse Lemma Let A CR let f Let f(x let ƒ lim f lim f(x limit mathematical induction Mean Value Theorem metric space monotone natural number neighborhood nonempty obtain open interval open set P₁ partition polynomial Proof properties Prove rational number reader real numbers result S₁ satisfy sequence of real Show that lim statement strictly increasing subinterval subset supremum Taylor's Theorem Theorem Let uniform convergence uniformly continuous upper bound whence it follows x₁ xn+1 y₁