a first course in analysis cambridge mathematical textbooks

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A First Course In Analysis

Author : John B. Conway
ISBN : 9781107173149
Genre : Mathematics
File Size : 21. 53 MB
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This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject.

A First Course In Mathematical Analysis

Author : J. C. Burkill
ISBN : 0521294681
Genre : Mathematics
File Size : 35. 74 MB
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This course is intended for students who have acquired a working knowledge of the calculus and are ready for a more systematic treatment which also brings in other limiting processes, such as the summation of infinite series and the expansion of trigonometric functions as power series.

A First Course In Mathematical Analysis

Author : David Alexander Brannan
ISBN : 9781139458955
Genre : Mathematics
File Size : 70. 76 MB
Format : PDF
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Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard university course on the subject.

A First Course In The Numerical Analysis Of Differential Equations

Author : A. Iserles
ISBN : 9780521734905
Genre : Mathematics
File Size : 51. 7 MB
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lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

A Second Course In Mathematical Analysis

Author : J. C. Burkill
ISBN : 0521523435
Genre : Mathematics
File Size : 40. 86 MB
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Classic calculus text reissued in Cambridge Mathematical Library. Clear, logical with many examples.

A Course In Abstract Analysis

Author : John B. Conway
ISBN : 9780821890837
Genre : Mathematics
File Size : 35. 33 MB
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This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. This material can easily be covered in a semester. The second half of the book treats basic functional analysis and can also be covered in a semester. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and C*-algebras. It concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single variable and the elements of metric spaces. Following the author's belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.

A Companion To Analysis

Author : Thomas William Körner
ISBN : 9780821834473
Genre : Mathematics
File Size : 83. 45 MB
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This book not only provides a lot of solid information about real analysis, it also answers those questions which students want to ask but cannot figure how to formulate. To read this book is to spend time with one of the modern masters in the subject. --Steven G. Krantz, Washington University, St. Louis One of the major assets of the book is Korner's very personal writing style. By keeping his own engagement with the material continually in view, he invites the reader to a similarly high level of involvement. And the witty and erudite asides that are sprinkled throughout the book are a real pleasure. --Gerald Folland, University of Washingtion, Seattle Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they hang together. This book provides such students with the coherent account that they need. A Companion to Analysis explains the problems which must be resolved in order to obtain a rigorous development of the calculus and shows the student how those problems are dealt with. Starting with the real line, it moves on to finite dimensional spaces and then to metric spaces. Readers who work through this text will be ready for such courses as measure theory, functional analysis, complex analysis and differential geometry. Moreover, they will be well on the road which leads from mathematics student to mathematician. Able and hard working students can use this book for independent study, or it can be used as the basis for an advanced undergraduate or elementary graduate course. An appendix contains a large number of accessible but non-routine problems to improve knowledge and technique.

Linear Analysis

Author : Béla Bollobás
ISBN : 0521655773
Genre : Mathematics
File Size : 40. 72 MB
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Revised and updated introduction to functional analysis.

A First Course In Fourier Analysis

Author : David W. Kammler
ISBN : 9780521883405
Genre : Mathematics
File Size : 71. 43 MB
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This book introduces applied mathematics through Fourier analysis, with applications to studying sampling theory, PDEs, probability, diffraction, musical tones, and wavelets.

A Course In Mathematical Analysis

Author : D. J. H. Garling
ISBN : 9781107032026
Genre : Mathematics
File Size : 32. 36 MB
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The first volume of three providing a full and detailed account of undergraduate mathematical analysis.

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