Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying. The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems usedat the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it intends to stimulate its readers to independent thought in discovering analysis. Prerequisites for accessing this book are arobust understanding of calculus and linear algebra." Helps instructors enhance lectures with problems beyond the classroom Helps prepare students for examinations Text encourages students to find different solutions to problems thanthose presented INDICE: Preface.- Elementary Logic and Set Theory.- Real Numbers.- Sequences.- Limits of Functions.- Continuity.- Differentiability.- Integration.- Series.- Metric Spaces.- Fundamentals of Topology.- Sequences and Series of Functions.- Index.- References.
- ISBN: 978-1-4419-1295-4
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 254
- Fecha Publicación: 01/12/2009
- Nº Volúmenes: 1
- Idioma: Inglés