Basic Elements of Real Analysis [Hardcover]

From the author of the highly-acclaimed A First Course in Real Analysis comes a volume designed specifically for a short one-semester course in real analysis. Many students of mathematics and the physical and computer sciences need a text that presents the most important material in a brief and elementary fashion. The author meets this need with such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series. There are proofs of the basic theorems on limits at a pace that is deliberate and detailed, backed by illustrative examples throughout and no less than 45 figures.From the author of the highly acclaimed A First Course in Real Analysis comes a volume designed specifically for a short one- semester course in real analysis. Many students of mathematics and those students who intend to study any of the physical sciences and computer science need a text that presents the most important material in a brief and elementary fashion. The author has included such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series. There are proofs of the basic theorems on limits at a pace that is deliberate and detailed. There are illustrative examples throughout with over 45 figures.The Real Number System.- Continuity and Limits.- Basic Properties of Functions on ?1.- Elementary Theory of Differentiation.- Elementary Theory of Integration.- Elementary Theory of Metric Spaces.- Differentiation and Integration in ?N.- Infinite Series.- The Derivative of an Integral.- The Riemann-Stieltjes Integral.- The Implicit Function Theorem. Lagrange Multipliers.- Vector Functions on ?N; The Theorems of Green and stokes. This book is intended for a shortened course aimed at students who intend to study the physical sciences or computer science. It covers the most important topics in an elementary way. ... The book can be rlC3