A Second Course in Mathematical Analysis

A Second Course in Mathematical Analysis
Author: J. C. Burkill
Publisher: Cambridge University Press
Total Pages: 536
Release: 2002-10-24
Genre: Mathematics
ISBN: 9780521523431

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

Mathematical Analysis

Mathematical Analysis
Author: Andrew Browder
Publisher: Springer Science & Business Media
Total Pages: 348
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461207150

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.

A Course of Mathematical Analysis

A Course of Mathematical Analysis
Author: Shanti Narayan | PK Mittal
Publisher: S. Chand Publishing
Total Pages: 610
Release: 2005-03
Genre: Mathematics
ISBN: 9788121904728

A Course of Mathematical Analysis

A Course of Modern Analysis

A Course of Modern Analysis
Author: E.T. Whittaker
Publisher: Courier Dover Publications
Total Pages: 624
Release: 2020-07-15
Genre: Mathematics
ISBN: 048684286X

Historic text by two great mathematicians consists of two parts, The Processes of Analysis and The Transcendental Functions. Geared toward students of analysis and historians of mathematics. 1920 third edition.

A First Course in Real Analysis

A First Course in Real Analysis
Author: Sterling K. Berberian
Publisher: Springer Science & Business Media
Total Pages: 249
Release: 2012-09-10
Genre: Mathematics
ISBN: 1441985484

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.

Advanced Calculus

Advanced Calculus
Author: Patrick Fitzpatrick
Publisher: American Mathematical Soc.
Total Pages: 610
Release: 2009
Genre: Mathematics
ISBN: 0821847910

"Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables."--pub. desc.

Foundations of Mathematical Analysis

Foundations of Mathematical Analysis
Author: Richard Johnsonbaugh
Publisher: Courier Corporation
Total Pages: 450
Release: 2012-09-11
Genre: Mathematics
ISBN: 0486134776

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.

A Course in Mathematical Analysis: Volume 2, Metric and Topological Spaces, Functions of a Vector Variable

A Course in Mathematical Analysis: Volume 2, Metric and Topological Spaces, Functions of a Vector Variable
Author: D. J. H. Garling
Publisher: Cambridge University Press
Total Pages: 335
Release: 2014-01-23
Genre: Mathematics
ISBN: 1107355427

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.

Mathematical Analysis

Mathematical Analysis
Author: Elias Zakon
Publisher: The Trillia Group
Total Pages: 436
Release: 2009-12-18
Genre: Mathematics
ISBN: 1931705038

Real Mathematical Analysis

Real Mathematical Analysis
Author: Charles Chapman Pugh
Publisher: Springer Science & Business Media
Total Pages: 445
Release: 2013-03-19
Genre: Mathematics
ISBN: 0387216847

Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.