## Yet Another Introduction to AnalysisMathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be well-motivated, relevant and practical. When such students reach higher education, the traditional development of analysis, often divorced from the calculus they learned at school, seems highly inappropriate. Shouldn't every step in a first course in analysis arise naturally from the student's experience of functions and calculus in school? And shouldn't such a course take every opportunity to endorse and extend the student's basic knowledge of functions? In Yet Another Introduction to Analysis, the author steers a simple and well-motivated path through the central ideas of real analysis. Each concept is introduced only after its need has become clear and after it has already been used informally. Wherever appropriate, new ideas are related to common topics in math curricula and are used to extend the reader's understanding of those topics. In this book the readers are led carefully through every step in such a way that they will soon be predicting the next step for themselves. In this way students will not only understand analysis, but also enjoy it. |

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User Review - amarcobio - LibraryThingI strongly recommend this book as an introduction to calculus, if you haven't took any undergrad course yet. I read it too late, though, so I couldn't make the most of it, but if I had to go to college again, I will certainly start with this book before adventuring in any calculus course. Read full review

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absolutely convergent approximately assume Bernoulli's inequality calculate chord consider continuous function convergent sequences converges to x0 converges with sum cosh decimal decreasing deduce definition of convergence differentiable at x0 diverges equal equation eventually Example Let exists an integer exp(x exponential function fact follows function g function given function whose domain function with domain gives gradient of PQ graph illustrated in/'s domain induction inequalities inverse function irrational number least upper bound Let/be limit local maximum maximum member mean value theorem minimum multiplying non-empty set non-negative over-estimates partition polynomial positive integer positive number proof prove radius of convergence range rational number real numbers rectangles result Rolle's theorem root sequence converges sequence xn series converges shown Similarly sine function sinh Solution stationary point strictly increasing subsequence supremum Taylor series Taylor's theorem that/is with/(x x2 x e XL x2