{"product_id":"introduction-to-real-analysis-9","title":"Introduction to Real Analysis","description":"\u003cp\u003eThis classic textbook has been used successfully by instructors and students for nearly three decades. This timely new edition offers minimal yet notable changes while retaining all the elements, presentation, and accessible exposition of previous editions. A list of updates is found in the Preface to this edition.\u003c\/p\u003e\u003cp\u003eThis text is based on the author’s experience in teaching graduate courses and the minimal requirements for successful graduate study. The text is understandable to the typical student enrolled in the course, taking into consideration the variations in abilities, background, and motivation. Chapters one through six have been written to be accessible to the average student,\u003c\/p\u003e\u003cp\u003ew hile at the same time challenging the more talented student through the exercises.\u003c\/p\u003e\u003cp\u003eChapters seven through ten assume the students have achieved some level of expertise in the subject. In these chapters, the theorems, examples, and exercises require greater sophistication and mathematical maturity for full understanding.\u003c\/p\u003e\u003cp\u003eIn addition to the standard topics the text includes topics that are not always included in comparable texts.\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003e \u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eChapter 6 contains a section on the Riemann-Stieltjes integral and a proof of Lebesgue’s t heorem providing necessary and sufficient conditions for Riemann integrability.\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e \u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eChapter 7 also includes a section on square summable sequences and a brief introduction to normed linear spaces.\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e \u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eC hapter 8 contains a proof of the Weierstrass approximation theorem using the method of\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eaapproximate identities.\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003e \u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eThe inclusion of Fourier series in the text allows the student to gain some exposure to this important subject.\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e \u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eThe final chapter includes a detailed treatment of Lebesgue measure and the Lebesgue integral, using inner and outer measure.\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e \u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eThe exercises at the end of each section reinforce the concepts.\u003c\/li\u003e\n\u003cli\u003e\n\u003cp\u003e \u003c\/p\u003e \u003c\/li\u003e\n\u003cli\u003eNotes provide historical comments or discuss additional topics.\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Product","offer_id":56680005632344,"sku":"9780367683931","price":67.99,"currency_code":"EUR","in_stock":true}],"url":"https:\/\/agendabookshop.com\/products\/introduction-to-real-analysis-9","provider":"Agenda Bookshop","version":"1.0","type":"link"}