Introduction to Real AnalysisAn elementary introduction to analysis. Limits the discussion to one variable, and presents detailed explanations and examples, focusing considerable attention on error estimation and other concepts relevant to computer science. |
Contents
CHAPTER ONE A Glimpse at Set Theory | 1 |
CHAPTER TWO The Real Numbers | 27 |
CHAPTER THREE Sequences | 69 |
Copyright | |
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Common terms and phrases
a₁ absolutely convergent approximation arbitrary Archimedean Property b₁ bounded function Cauchy sequence cluster point conclude continuous function convergent sequence converges uniformly Corollary decimal defined Definition denote derivative differentiable divergent elements end point example Exercises for Section f is continuous Figure finite number follows from Theorem function f ƒ and g ƒ is integrable given Hence implies improper integral inequality infinite Lemma Let A CR let f Let f(x let ƒ lim f lim f(x lim ƒ limit mathematical induction Mean Value Theorem monotone natural number neighborhood obtain open sets partition polynomial Proof properties Prove rational number reader result Riemann integral satisfy sequence of real Show that lim strictly increasing strictly positive subinterval subset sup f(x Suppose that ƒ supremum Taylor's Theorem uniform convergence uniformly continuous upper bound whence it follows x₁ xn+1