Introduction to real analysis

using An Extremely Clear And Informal Approach, This Book Introduces Readers To A Rigorous Understanding Of Mathematical Analysis And Presents Challenging Math Concepts As Clearly As Possible. The Real Number System. Differential Calculus Of Functions Of One Variable. Riemann Integral Functions Of One Variable. Integral Calculus Of Real-valued Functions. Metric Spaces. For Those Who Want To Gain An Understanding Of Mathematical Analysis And Challenging Mathematical Concepts. This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1-5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1-5. Annotation Introducing students to an understanding of mathematical analysis, this text aims to present mathematical concepts clearly. It also provides students with the background required for insight into more advanced courses in pure and applied mathematics. It is intended for two-semester, junior/senior-level courses in introductory real analysis