Undergraduate analysis : a working textbook /
Aisling McCluskey (Senior Lecturer in Mathematics, National University of Ireland, Galway), Brian McMaster (Honorary Senior Lecturer, Queen's University Belfast).
- First edition.
- 381 pages : illustrations ; 24 cm
Includes bibliographical references (page 377) and index.
Preliminaries -- Limit of a sequence - an idea, a definition, a tool -- Interlude: different kinds of numbers -- Up and down - increasing and decreasing sequences -- Special (or specially awkward) examples -- Endless sums - a first look at series -- Continuous functions - the domain thinks that the graph is unbroken -- Limit of a function -- Epsilontics and functions -- Infinity and function limits -- Differentiation - the slope of a graph -- The Cauchy condition - sequences whose terms pack tightly together -- More about series -- Uniform continuity - continuity's global cousin -- Differentiation - mean value theorems, power series -- Riemann integration - area under a graph -- The elementary functions revisited -- Exercises: for additional practice.