A Second Course in Mathematical Analysis
Title | A Second Course in Mathematical Analysis PDF eBook |
Author | J. C. Burkill |
Publisher | Cambridge University Press |
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
Title | A Companion to Analysis PDF eBook |
Author | Thomas William Körner |
Publisher | American Mathematical Soc. |
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
Title | A Second Course in Complex Analysis PDF eBook |
Author | William A. Veech |
Publisher | Courier Corporation |
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
Title | Mathematical Analysis PDF eBook |
Author | Andrew Browder |
Publisher | Springer Science & Business Media |
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
Title | A Second Course in Mathematical Analysis PDF eBook |
Author | Dorairaj Somasundaram |
Publisher | Alpha Science International, Limited |
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 First Course in Numerical Analysis
Title | A First Course in Numerical Analysis PDF eBook |
Author | Anthony Ralston |
Publisher | Courier Corporation |
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
Title | Calculus Deconstructed PDF eBook |
Author | Zbigniew H. Nitecki |
Publisher | American Mathematical Society |
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.