| Description |
1 online resource |
| Physical Medium |
polychrome |
| Description |
text file |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
2.9 POSTSCRIPT: to infinity2.10 Important note on 'elementary functions'; 3 Interlude: different kinds of numbers; 3.1 Sets; 3.2 Intervals, max and min, sup and inf; 3.3 Denseness; 4 Up and down -- increasing and decreasing sequences; 4.1 Monotonic bounded sequences must converge; 4.2 Induction: infinite returns for finite effort; 4.3 Recursively defined sequences; 4.4 POSTSCRIPT: The epsilontics game -- the 'fifth factor of difficulty'; 5 Sampling a sequence -- subsequences; 5.1 Introduction; 5.2 Subsequences; 5.3 Bolzano-Weierstrass: the overcrowded interval |
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Cover; Undergraduate Analysis: A Working Textbook; Copyright; Dedication; Preface; Contents; A Note to the Instructor; A Note to the Student Reader; 1 Preliminaries; 1.1 Real numbers; 1.2 The basic rules of inequalities -- a checklist of things you probably know already; 1.3 Modulus; 1.4 Floor; 2 Limit of a sequence -- an idea, a definition, a tool; 2.1 Introduction; 2.2 Sequences, and how to write them; 2.3 Approximation; 2.4 Infinite decimals; 2.5 Approximating an area; 2.6 A small slice of π; 2.7 Testing limits by the definition; 2.8 Combining sequences; the algebra of limits |
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6 Special (or specially awkward) examples6.1 Introduction; 6.2 Important examples of convergence; 7 Endless sums -- a first look at series; 7.1 Introduction; 7.2 Definition and easy results; 7.3 Big series, small series: comparison tests; 7.4 The root test and the ratio test; 8 Continuous functions -- the domain thinks that the graph is unbroken; 8.1 Introduction; 8.2 An informal view of continuity; 8.3 Continuity at a point; 8.4 Continuity on a set; 8.5 Key theorems on continuity; 8.6 Continuity of the inverse; 9 Limit of a function; 9.1 Introduction; 9.2 Limit of a function at a point |
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10 Epsilontics and functions10.1 The epsilontic view of function limits; 10.2 The epsilontic view of continuity; 10.3 One-sided limits; 11 Infinity and function limits; 11.1 Limit of a function as x tends to infinity or minus infinity; 11.2 Functions tending to infinity or minus infinity; 12 Differentiation -- the slope of the graph; 12.1 Introduction; 12.2 The derivative; 12.3 Up and down, maximum and minimum: for differentiable functions; 12.4 Higher derivatives; 12.5 Alternative proof of the chain rule; 13 The Cauchy condition -- sequences whose terms pack tightly together |
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13.1 Cauchy equals convergent14 More about series; 14.1 Absolute convergence; 14.2 The 'robustness' of absolutely convergent series; 14.3 Power series; 15 Uniform continuity -- continuity's global cousin; 15.1 Introduction; 15.2 Uniformly continuous functions; 15.3 The bounded derivative test; 16 Differentiation -- mean value theorems, power series; 16.1 Introduction; 16.2 Cauchy and l'Hôpital; 16.3 Taylor series; 16.4 Differentiating a power series; 17 Riemann integration -- area under a graph; 17.1 Introduction |
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17.2 Riemann integrability -- how closely can rectangles approximate areas under graphs? |
| Summary |
An innovative self-contained Analysis textbook for undergraduates, that takes advantage of proven successful educational techniques. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Mathematical analysis.
|
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Mathematical analysis. |
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MATHEMATICS -- Calculus. |
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MATHEMATICS -- Mathematical Analysis. |
| Genre/Form |
Electronic books.
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| Added Author |
McMaster, Brian, author.
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| Other Form: |
Print version: McCluskey, Aisling. Undergraduate analysis. Oxford, United Kingdom : Oxford University Press, 2018 0198817568 9780198817567 (OCoLC)1013489598 |
| ISBN |
9780192549839 (electronic book) |
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0192549839 (electronic book) |
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9780198817574 (print) |
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0198817568 |
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9780198817567 |
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0198817576 |
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