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Author: Murray H. Protter Publisher: Springer Science & Business Media ISBN: 1441987444 Category : Mathematics Languages : en Pages : 536

Book Description
Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation.

Author: Murray H. Protter Publisher: Springer Science & Business Media ISBN: 1441987444 Category : Mathematics Languages : en Pages : 536

Book Description
Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation.

Author: Sterling K. Berberian Publisher: Springer Science & Business Media ISBN: 1441985484 Category : Mathematics Languages : en Pages : 240

Book Description
Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.

Author: Murray H. Protter Publisher: ISBN: Category : Mathematical analysis Languages : en Pages : 536

Book Description
This book is designed for a first course in real analysis which follows the standard course in elementary calculus. Since many students encounter rigorous mathematical theory for the first time in this course, the authors include such elementary topics as the axioms of algebra and their immediate consequences and proofs of theorems on limits. The pace is deliberately slow, the proofs are detailed. The emphasis of the presentation is on theory, but the books also contains a full treatment (with many illustrative examples and exercises) of the standard topics in infinite series, Fourier series, multidimensional calculus, elements of metric spaces, and vector field theory. There are many problems which require the student to learn techniques of proofs and the standard tools of analysis. -- Back cover.

Author: David Alexander Brannan Publisher: Cambridge University Press ISBN: 1139458957 Category : Mathematics Languages : en Pages :

Book Description
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.

Author: Russell A. Gordon Publisher: Pearson ISBN: Category : Mathematical analysis Languages : en Pages : 408

Book Description
This text presents ideas of elementary real analysis, with chapters on real numbers, sequences, limits and continuity, differentiation, integration, infinite series, sequences and series of functions, and point-set topology. Appendices review essential ideas of mathematical logic, sets and functions, and mathematical induction. Students are required to confront formal proofs. Some background in calculus or linear or abstract algebra is assumed. This second edition adds material on functions of bounded variation, convex functions, numerical methods of integration, and metric spaces. There are 1,600 exercises in this edition, an addition of some 120 pages. c. Book News Inc.

Author: J. C. Burkill Publisher: Cambridge University Press ISBN: 9780521294683 Category : Mathematics Languages : en Pages : 200

Book Description
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.

Author: Dorairaj Somasundaram Publisher: ISBN: 9788173190643 Category : Mathematics Languages : en Pages : 616

Book Description
Intends to serve as a textbook in Real Analysis at the Advanced Calculus level. This book includes topics like Field of real numbers, Foundation of calculus, Compactness, Connectedness, Riemann integration, Fourier series, Calculus of several variables and Multiple integrals are presented systematically with diagrams and illustrations.

Author: Dr Sathisha A B Publisher: Blue Rose Publishers ISBN: 9356286590 Category : Education Languages : en Pages : 380

Book Description
This book is suitable for undergraduate and post graduate students ofn pure and applied mathematics. An attempt has been made to present detailed information of basic topics in Real analysis in a simple way so that it is easily understandable to the users. The book is designed as a selfâ€“contained comprehensive text. Each topic is treated in a systematic manner. The book focuses on a Real number system, the sequence of real numbers, the series of real numbers, limits and continuity, differentiation and means value theorems. A large number of theorems and related problems are included for a better understanding of the concepts. It also includes exercise problems at the end of every chapter. The book is useful for students, faculty and those who are actively involved in Research in the areas requiring basic knowledge of Real Analysis.