Description
Book SynopsisAnalysis underpins calculus, much as calculus underpins virtually all mathematical sciences. A sound understanding of analysis'' results and techniques is therefore valuable for a wide range of disciplines both within mathematics itself and beyond its traditional boundaries. This text seeks to develop such an understanding for undergraduate students on mathematics and mathematically related programmes. Keenly aware of contemporary students'' diversity of motivation, background knowledge and time pressures, it consistently strives to blend beneficial aspects of the workbook, the formal teaching text, and the informal and intuitive tutorial discussion.The authors devote ample space and time for development of confidence in handling the fundamental ideas of the topic. They also focus on learning through doing, presenting a comprehensive range of examples and exercises, some worked through in full detail, some supported by sketch solutions and hints, some left open to the reader''s initiat
Trade ReviewThe clear, concise writing makes this book ideal for equipping undergraduates with a solid conceptual framework for approaching analysis rigorously and confidently. * V.K. Chellamuthu, CHOICE *
Table of Contents1: Preliminaries 2: Limit of a sequence, an idea, a definition, a tool 3: Interlude: different kinds of numbers 4: Up and down - increasing and decreasing sequences 5: Sampling a sequence - subsequences 6: Special (or specially awkward) examples 7: Endless sums - a first look at series 8: Continuous functions - the domain thinks that the graph is unbroken 9: Limit of a function 10: Epsilontics and functions 11: Infinity and function limits 12: Differentiation - the slope of the graph 13: The Cauchy condition - sequences whose terms pack tightly together 14: More about series 15: Uniform continuity - continuity's global cousin 16: Differentiation - mean value theorems, power series 17: Riemann integration - area under a graph 18: The elementary functions revisited
