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 : 66. 60 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 : David Alexander Brannan
ISBN : 9781139458955
Genre : Mathematics
File Size : 70. 63 MB
Format : PDF, ePub
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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 Mathematical Analysis

Author : J. C. Burkill
ISBN : 0521294681
Genre : Mathematics
File Size : 67. 69 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 Second Course In Mathematical Analysis

Author : J. C. Burkill
ISBN : 0521523435
Genre : Mathematics
File Size : 89. 99 MB
Format : PDF, ePub
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Classic calculus text reissued in Cambridge Mathematical Library. Clear, logical with many examples.

A First Course In The Numerical Analysis Of Differential Equations

Author : A. Iserles
ISBN : 9780521734905
Genre : Mathematics
File Size : 46. 34 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.

Linear Analysis

Author : Béla Bollobás
ISBN : 0521655773
Genre : Mathematics
File Size : 59. 31 MB
Format : PDF
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Revised and updated introduction to functional analysis.

A Companion To Analysis

Author : Thomas William Körner
ISBN : 9780821834473
Genre : Mathematics
File Size : 30. 73 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.

A First Course In Harmonic Analysis

Author : Anton Deitmar
ISBN : 9781475738346
Genre : Mathematics
File Size : 51. 29 MB
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This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.

A Course Of Modern Analysis

Author : E. T. Whittaker
ISBN : 9781107268586
Genre : Mathematics
File Size : 32. 92 MB
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This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principal transcendental functions.

A Second Course In Linear Algebra

Author : Stephan Ramon Garcia
ISBN : 9781107103818
Genre : Mathematics
File Size : 28. 65 MB
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Linear algebra is a fundamental tool in many fields, including mathematics and statistics, computer science, economics, and the physical and biological sciences. This undergraduate textbook offers a complete second course in linear algebra, tailored to help students transition from basic theory to advanced topics and applications. Concise chapters promote a focused progression through essential ideas, and contain many examples and illustrative graphics. In addition, each chapter contains a bullet list summarising important concepts, and the book includes over 600 exercises to aid the reader's understanding. Topics are derived and discussed in detail, including the singular value decomposition, the Jordan canonical form, the spectral theorem, the QR factorization, normal matrices, Hermitian matrices (of interest to physics students), and positive definite matrices (of interest to statistics students).

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