A First Course in Mathematical Analysis PDF Download

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

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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: M.H. Protter
Publisher: Springer Science & Business Media
ISBN: 1461599903
Category : Mathematics
Languages : en
Pages : 520

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Book Description
The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.

Author: George Pedrick
Publisher: Springer Science & Business Media
ISBN: 1441985549
Category : Mathematics
Languages : en
Pages : 293

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Book Description
This text on advanced calculus discusses such topics as number systems, the extreme value problem, continuous functions, differentiation, integration and infinite series. The reader will find the focus of attention shifted from the learning and applying of computational techniques to careful reasoning from hypothesis to conclusion. The book is intended both for a terminal course and as preparation for more advanced studies in mathematics, science, engineering and computation.

Author: John B. Conway
Publisher: Cambridge University Press
ISBN: 1107173140
Category : Mathematics
Languages : en
Pages : 357

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Book Description
This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.

Author: Sterling K. Berberian
Publisher: Springer Science & Business Media
ISBN: 1441985484
Category : Mathematics
Languages : en
Pages : 249

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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: J. C. Burkill
Publisher: Cambridge University Press
ISBN: 9780521523431
Category : Mathematics
Languages : en
Pages : 536

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Book Description
A classic calculus text reissued in the Cambridge Mathematical Library. Clear and logical, with many examples.

Author: Andrew Browder
Publisher: Springer Science & Business Media
ISBN: 1461207150
Category : Mathematics
Languages : en
Pages : 348

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Book Description
Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.

Author: Richard Johnsonbaugh
Publisher: Courier Corporation
ISBN: 0486134776
Category : Mathematics
Languages : en
Pages : 450

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Book Description
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

Author: Vladimir A. Zorich
Publisher: Springer Science & Business Media
ISBN: 9783540403869
Category : Mathematics
Languages : en
Pages : 610

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Book Description
This work by Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions.

Author: Anthony Ralston
Publisher: Courier Corporation
ISBN: 9780486414546
Category : Mathematics
Languages : en
Pages : 644

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Book Description
Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.