Complex Variables Demystified
by David McMahon
from McGraw-Hill Professional
Take the complication out of COMPLEX VARIABLES
Ready to learn the fundamentals of complex variables but can't seem to get your brain to function on the right level? No problem! Add Complex Variables Demystified to the equation and you'll exponentially increase your chances of understanding this fascinating subject.
Written in an easy-to-follow format, this book begins by covering complex numbers, functions, limits, and continuity, and the Cauchy-Riemann equations. You'll delve into sequences, Laurent series, complex integration, and residue theory. Then it's on to conformal mapping, transformations, and boundary value problems. Hundreds of examples and worked equations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.
This fast and easy guide offers:
- Numerous figures to illustrate key concepts
- Sample problems with worked solutions
- Coverage of Cauchy-Riemann equations and the Laplace transform
- Chapters on the Schwarz-Christoffel transformation and the gamma and zeta functions
- A time-saving approach to performing better on an exam or at work
Simple enough for a beginner, but challenging enough for an advanced student, Complex Variables Demystified is your integral tool for understanding this essential mathematics topic.
Elements of the Theory of Functions and Functional Analysis
by A. N. Kolmogorov
from Dover Publications
Understanding Analysis
by Stephen Abbott
from Springer
This book outlines an elementary, one-semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.
Riemann's Zeta Function
by Harold M. Edwards
from Dover Publications
Infinite Dimensional Analysis: A Hitchhiker's Guide
by Charalambos D. Aliprantis
from Springer
This monograph presents a complete and rigorous study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but does not have an extensive background and does not plan to make a career as a functional analyst. It develops the topological structures in connection with measure theory, convexity, Banach lattices, integration, correspondences (multifunctions), and the analytic approach to Markov processes. Many of the results were previously available only in works scattered throughout the literature. The choice of material was motivated from problems in control theory and economics, although the material is more applicable than applied.
A Geometric Approach to Differential Forms
by David Bachman
from Birkhäuser Boston
The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the sophomore undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually.
Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions. A centerpiece of the text is the generalized Stokes' theorem. Although this theorem implies all of the classical integral theorems of vector calculus, it is far easier for students to both comprehend and remember.
The text is designed to support three distinct course tracks: the first as the primary textbook for third semester (multivariable) calculus, suitable for anyone with a year of calculus; the second is aimed at students enrolled in sophomore-level vector calculus; while the third targets advanced undergraduates and beginning graduate students in physics or mathematics, covering more advanced topics such as Maxwell's equations, foliation theory, and cohomology.
Containing excellent motivation, numerous illustrations and solutions to selected problems in an appendix, the material has been tested in the classroom along all three potential course tracks.
Problems and Solutions for Undergraduate Analysis (Undergraduate Texts in Mathematics)
by Rami Shakarchi
from Springer
This volume contains all the exercises and their solutions for Lang's second edition of UNDERGRADUATE ANALYSIS. The wide variety of exercises, which range from computational to more conceptual and which are of varying difficulty, cover the following subjects and more: real numbers, limits, continuous functions, differentiation and elementary integration, normed vector spaces, compactness, series, integration in one variable, improper integrals, convolutions, Fourier series and the Fourier integral, functions in n-space, derivatives in vector spaces, inverse and implicit mapping theorem, ordinary differential equations, multiple integrals and differential forms. This volume also serves as an independent source of problems with detailed answers beneficial for anyone interested in learning analysis. Intermediary steps and original drawings provided by the author assists students in their mastery of problem solving techniques and increases their overall comprehension of the subject matter.
Real Mathematical Analysis
by Charles Chapman Pugh
from Springer
In this new introduction to undergraduate real analysis the author takes a different approach from past presentations 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 such as Dieudonne, Littlewood, and Osserman. This book is based on the honors version of a course which the author has taught many times over the last 35 years at Berkeley. The book contains an excellent selection of more than 500 exercises.
Introductory Functional Analysis with Applications
by Erwin Kreyszig
from Wiley
Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis.
Analysis (Graduate Studies in Mathematics)
by Elliott H. Lieb
from American Mathematical Society
Significantly revised and expanded, this new Second Edition provides readers at all levels - from beginning students to practicing analysts - with the basic concepts and standard tools necessary to solve problems of analysis, and how to apply these concepts to research in a variety of areas. Authors Elliott Lieb and Michael Loss take you quickly from basic topics to methods that work successfully in mathematics and its applications. While omitting many usual typical textbook topics, "Analysis" includes all necessary definitions, proofs, explanations, examples, and exercises to bring the reader to an advanced level of understanding with a minimum of fuss, and, at the same time, doing so in a rigorous and pedagogical way. Many topics that are useful and important, but usually left to advanced monographs, are presented in "Analysis", and these give the beginner a sense that the subject is alive and growing.This new Second Edition incorporates numerous changes since the publication of the original 1997 edition and includes: a new chapter on eigenvalues that covers the min-max principle, semi-classical approximation, coherent states, Lieb-Thirring inequalities, and more; extensive additions to chapters covering Sobolev Inequalities, including the Nash and Log Sobolev inequalities; new material on Measure and Integration; many new exercises; and, much more. ..The Second Edition continues its no-nonsense approach to the topic that has made it one of the best selling books on the subject. It is an authoritative, straight-forward volume that readers - from the graduate student, to the professional mathematician, to the physicist or engineer using analytical methods - will find useful both as a reference and as a guide to real problem solving.About the authors: Elliott Lieb is Professor of Mathematics and Physics at Princeton University and is a member of the US, Austrian, and Danish Academies of Science. He is also the recipient of several prizes including the 1988 AMS/SIAM Birkhoff Prize. Michael Loss is Professor of Mathematics at the Georgia Institute of Technology.
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