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 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.

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.

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.

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 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.

Mathematical Analysis

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

Mathematical Analysis

Mathematical Analysis
Author: Bernd S. W. Schröder
Publisher: John Wiley & Sons
Total Pages: 584
Release: 2008-01-28
Genre: Mathematics
ISBN: 9780470226766

A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.

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.