Real Analysis: A First Course, 2nd Edition

ISBN: 0201437279

Author: Gordon, Russell

Condition: New

Real Analysis, 2/e is a carefully worded narrative that presents the ideas of elementary real analysis while keeping the perspective of a student in mind. The order and flow of topics has been preserved, but the sections have been reorganized somewhat so that related ideas are grouped together better. A few additional topics have been added; most notably, functions of bounded variation, convex function, numerical methods of integration, and metric spaces. The biggest change is the number of exercises; there are now more than 1600 exercises in the text.

• Introductory material, such as the study of sets, functions, relations, and mathematical induction has been kept to a minimum and is presented in context for students to acquire a working knowledge. The three appendices go into more depth with introductory material, without bogging down the course. | Focus of the text is on the basic notation of real analysis. Peripheral material has been kept to a minimum to avoid overwhelming students with too much information. | Topological concepts, omitted from the main body of the text, are presented in a separate chapter at the end of the text for the benefit of students going on in mathematics. Although topological concepts are necessary in Rn, Gordon motivates the introduction of topology in R using questions and problems. | The Riemann approach to the integral is carried out in detail. This approach is used exclusively, as it provides a consistent definition of the integral and is in keeping with the integral as it is usually defined in calculus. | Gordon carefully words and presents proofs, so they are clear and understandable to the students. Parts of some proofs are left as exercises, so that students must participate in the development of the material.