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.

A Companion to Analysis

A Companion to Analysis
Author: Thomas William Körner
Publisher: American Mathematical Soc.
Total Pages: 608
Release: 2004
Genre: Mathematics
ISBN: 0821834479

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 Second Course in Complex Analysis

A Second Course in Complex Analysis
Author: William A. Veech
Publisher: Courier Corporation
Total Pages: 257
Release: 2014-08-04
Genre: Mathematics
ISBN: 048615193X

A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. The material is largely classical, with particular emphasis on the geometry of complex mappings. Author William A. Veech, the Edgar Odell Lovett Professor of Mathematics at Rice University, presents the Riemann mapping theorem as a special case of an existence theorem for universal covering surfaces. His focus on the geometry of complex mappings makes frequent use of Schwarz's lemma. He constructs the universal covering surface of an arbitrary planar region and employs the modular function to develop the theorems of Landau, Schottky, Montel, and Picard as consequences of the existence of certain coverings. Concluding chapters explore Hadamard product theorem and prime number theorem.

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 Second Course in Mathematical Analysis

A Second Course in Mathematical Analysis
Author: Dorairaj Somasundaram
Publisher: Alpha Science International, Limited
Total Pages: 0
Release: 2010
Genre: Mathematical analysis
ISBN: 9781842655337

A Second Course in Mathematical Analysis makes an in-depth study of Infinite series, Double sequences and series, power series, sequences and series of functions, Functions of bounded variation, Riemann - Stieltjes integrals, Lebesgue integrals, Fourier series, Multivariable differential calculus, Implicit functions and Extremum problems.

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.

Introduction to Analysis

Introduction to Analysis
Author: Edward Gaughan
Publisher: American Mathematical Soc.
Total Pages: 258
Release: 2009
Genre: Mathematics
ISBN: 0821847872

"The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section."--pub. desc.

Mathematical Analysis I

Mathematical Analysis I
Author: Vladimir A. Zorich
Publisher: Springer Science & Business Media
Total Pages: 610
Release: 2004-01-22
Genre: Mathematics
ISBN: 9783540403869

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.

A First Course in Numerical Analysis

A First Course in Numerical Analysis
Author: Anthony Ralston
Publisher: Courier Corporation
Total Pages: 644
Release: 2001-01-01
Genre: Mathematics
ISBN: 9780486414546

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.

Calculus Deconstructed

Calculus Deconstructed
Author: Zbigniew H. Nitecki
Publisher: American Mathematical Society
Total Pages: 491
Release: 2022-01-11
Genre: Mathematics
ISBN: 1470466759

Calculus Deconstructed is a thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous exposure to calculus techniques but not to methods of proof. This book is appropriate for a beginning Honors Calculus course assuming high school calculus or a "bridge course" using basic analysis to motivate and illustrate mathematical rigor. It can serve as a combination textbook and reference book for individual self-study. Standard topics and techniques in single-variable calculus are presented in context of a coherent logical structure, building on familiar properties of real numbers and teaching methods of proof by example along the way. Numerous examples reinforce both practical and theoretical understanding, and extensive historical notes explore the arguments of the originators of the subject. No previous experience with mathematical proof is assumed: rhetorical strategies and techniques of proof (reductio ad absurdum, induction, contrapositives, etc.) are introduced by example along the way. Between the text and exercises, proofs are available for all the basic results of calculus for functions of one real variable.