{"product_id":"welcome-to-real-analysis-continuity-and-calculus-distance-and-dynamics-9781470464547","title":"Welcome to Real Analysis: Continuity and Calculus, Distance and Dynamics","description":"\u003cp\u003e\u003c\/p\u003e\u003cblockquote\u003eThis book is intended for an introductory undergraduate course in real analysis. It uses the real line, $n$-dimensional Euclidean space, sequence and function spaces, and single-variable calculus to prove and extend results. It also includes exercises and pedagogical innovations, such as Reading Questions and two concluding chapters on dynamical systems and fractals. \u003c\/blockquote\u003e\u003cp\u003e\u003cstrong\u003eFormat\u003c\/strong\u003e: Paperback \/ softback\u003cbr\u003e\u003cstrong\u003eLength\u003c\/strong\u003e: 370 pages\u003cbr\u003e\u003cstrong\u003ePublication date\u003c\/strong\u003e: 30 April 2022\u003cbr\u003e\u003cstrong\u003ePublisher\u003c\/strong\u003e: American Mathematical Society\u003cbr\u003e\u003c\/p\u003e \u003cp\u003e\u003cbr\u003eWelcome to Real Analysis, a comprehensive textbook designed for an introductory undergraduate course in real analysis. This text offers a thorough exploration of the fundamental concepts and theories of the field, with a focus on the setting of the general metric space. Throughout the book, readers will encounter a rich blend of the real line and $n$-dimensional Euclidean space, as well as sequence and function spaces, all of which play crucial roles in the development of real analysis.\u003cbr\u003e\u003cbr\u003eThe central theme of the book is to prove and extend results from single-variable calculus, providing a solid foundation for the more abstract ideas that follow. The author employs a clear and engaging writing style, making complex concepts accessible to students with a strong mathematical background. Each chapter is accompanied by a multitude of exercises, designed to reinforce the understanding of the material and encourage critical thinking.\u003cbr\u003e\u003cbr\u003eOne of the notable features of this text is its emphasis on motivation. The author takes the time to explain the relevance and practical applications of the theories and concepts discussed, making the subject matter more engaging and meaningful. For instance, the contraction mapping principle is used to prove an existence and uniqueness theorem for solutions of ordinary differential equations, while the continuity of the integration operator on the space of continuous functions on a compact interval paves the way for results about power series.\u003cbr\u003e\u003cbr\u003eThe exposition is exceptionally clear and well-motivated, with a wide variety of exercises and pedagogical innovations. For example, each chapter includes Reading Questions that allow students to assess their understanding of the material covered. In addition to the standard material in a first real analysis course, the book concludes with two concluding chapters on dynamical systems and fractals, serving as illustrations of the power and versatility of the theory developed throughout the text.\u003cbr\u003e\u003cbr\u003eIn conclusion, Real Analysis is an excellent resource for students embarking on a journey into the world of real analysis. With its comprehensive coverage, clear exposition, and engaging exercises, this text provides a solid foundation for understanding the fundamental concepts and theories of the field. Whether you are a mathematics student or a professional seeking to expand your knowledge in this area, this book is an invaluable tool for your academic pursuits.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWeight\u003c\/strong\u003e: 672g\u003cbr\u003e\u003cstrong\u003eDimension\u003c\/strong\u003e: 254 x 178 (mm)\u003cbr\u003e\u003cstrong\u003eISBN-13\u003c\/strong\u003e: 9781470464547\u003c\/p\u003e","brand":"Benjamin B. Kennedy","offers":[{"title":"Paperback \/ softback","offer_id":44310056272122,"sku":"9781470464547","price":54.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/4297\/2845\/products\/1688127433168_book.jpg?v=1688198770","url":"https:\/\/shulphink.com\/products\/welcome-to-real-analysis-continuity-and-calculus-distance-and-dynamics-9781470464547","provider":"Shulph Ink","version":"1.0","type":"link"}