A Companion to Analysis

A Second First and First Second Course in Analysis

Author: Thomas William Körner

Publisher: American Mathematical Soc.

ISBN: 0821834479

Category: Mathematics

Page: 590

View: 5254

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.


From Concepts to Applications

Author: Jean-Paul Penot

Publisher: Springer

ISBN: 331932411X

Category: Mathematics

Page: 669

View: 8920

This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems. In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena. Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book’s style and layout make it suitable for use in several courses, while its self-contained character makes it appropriate for self-study.

Understanding Analysis

Author: Stephen Abbott

Publisher: Springer

ISBN: 1493927124

Category: Mathematics

Page: 312

View: 4722

This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.

Elements of Real Analysis

Author: Charles G. Denlinger

Publisher: Jones & Bartlett Learning

ISBN: 0763779474

Category: Mathematics

Page: 739

View: 6425

Elementary Real Analysis is a core course in nearly all mathematics departments throughout the world. It enables students to develop a deep understanding of the key concepts of calculus from a mature perspective. Elements of Real Analysis is a student-friendly guide to learning all the important ideas of elementary real analysis, based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors. It avoids the compact style of professional mathematics writing, in favor of a style that feels more comfortable to students encountering the subject for the first time. It presents topics in ways that are most easily understood, yet does not sacrifice rigor or coverage. In using this book, students discover that real analysis is completely deducible from the axioms of the real number system. They learn the powerful techniques of limits of sequences as the primary entry to the concepts of analysis, and see the ubiquitous role sequences play in virtually all later topics. They become comfortable with topological ideas, and see how these concepts help unify the subject. Students encounter many interesting examples, including "pathological" ones, that motivate the subject and help fix the concepts. They develop a unified understanding of limits, continuity, differentiability, Riemann integrability, and infinite series of numbers and functions.

Behavioral Research and Analysis

An Introduction to Statistics within the Context of Experimental Design, Fourth Edition

Author: Max Vercruyssen,Hal W. Hendrick

Publisher: CRC Press

ISBN: 1439897514

Category: Mathematics

Page: 299

View: 5448

Now in its fourth edition, Behavioral Research and Analysis: An Introduction to Statistics within the Context of Experimental Design presents an overview of statistical methods within the context of experimental design. It covers fundamental topics such as data collection, data analysis, interpretation of results, and communication of findings. New in the Fourth Edition: Extensive improvements based on suggestions from those using this book in the classroom Statistical procedures that have been developed and validated since the previous edition Each chapter in the body now contains relevant key words, chapter summaries, key word definitions, and end of chapter exercises (with answers) Revisions to include recent changes in the APA Style Manual When looking for a book for their own use, the authors found none that were totally suitable. They found books that either reviewed the basics of behavioral research and experimental design but provided only cursory coverage of statistical methods or they provided coverage of statistical methods with very little coverage of the research context within which these methods are used. No single resource provided coverage of methodology, statistics, and communication skills. In a classic example of necessity being the mother of invention, the authors created their own. This text is ideal for a single course that reviews research methods, essential statistics through multi-factor analysis of variance, and thesis (or major project) preparation without discussion of derivation of equations, probability theory, or mathematic proofs. It focuses on essential information for getting a research project completed without prerequisite math or statistics training. It has been revised many times to help students at a variety of academic levels (exceptional high school students, undergraduate honors students, masters students, doctoral students, and post-doctoral fellows) across varied academic disciplines (e.g., human factors and ergonomics, behavioral and social sciences, natural sciences, engineering, exercise and sport sciences, business and management, industrial hygiene and safety science, health and medical sciences, and more). Illustrating how to plan, prepare, conduct, and analyze an experimental or research report, the book emphasizes explaining statistical procedures and interpreting obtained results without discussing the derivation of equations or history of the method. Destined to spend more time on your desk than on the shelf, the book will become the single resource you reach for again and again when conducting scientific research and reporting it to the scientific community.

Mathematical Statistics with Applications in R

Author: Kandethody M. Ramachandran,Chris P. Tsokos

Publisher: Elsevier

ISBN: 012417132X

Category: Mathematics

Page: 826

View: 4123

Mathematical Statistics with Applications in R, Second Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining the discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem solving in a logical manner. This book provides a step-by-step procedure to solve real problems, making the topic more accessible. It includes goodness of fit methods to identify the probability distribution that characterizes the probabilistic behavior or a given set of data. Exercises as well as practical, real-world chapter projects are included, and each chapter has an optional section on using Minitab, SPSS and SAS commands. The text also boasts a wide array of coverage of ANOVA, nonparametric, MCMC, Bayesian and empirical methods; solutions to selected problems; data sets; and an image bank for students. Advanced undergraduate and graduate students taking a one or two semester mathematical statistics course will find this book extremely useful in their studies. Step-by-step procedure to solve real problems, making the topic more accessible Exercises blend theory and modern applications Practical, real-world chapter projects Provides an optional section in each chapter on using Minitab, SPSS and SAS commands Wide array of coverage of ANOVA, Nonparametric, MCMC, Bayesian and empirical methods

Finite Elements and Fast Iterative Solvers

With Applications in Incompressible Fluid Dynamics

Author: Howard C. Elman,David J. Silvester,Andrew J. Wathen

Publisher: Oxford University Press (UK)

ISBN: 0199678804

Category: Mathematics

Page: 479

View: 9289

This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory" provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

The Elgar Companion to the Chicago School of Economics

Author: Ross B. Emmett

Publisher: Edward Elgar Publishing

ISBN: 1849806667

Category: Business & Economics

Page: 360

View: 9820

Many know the Chicago School of Economics and its association with Milton Friedman, George Stigler, Ronald Coase and Gary Becker. But few know the School's history and the full scope of its scholarship. In this Companion, leading scholars examine its history and key figures, as well as provide surveys of the School's contributions to central aspects of economics, including: price theory, monetary theory, labor and economic history. The volume examines the School's traditions of applied welfare theory and law and economics while providing a glimpse into emerging research on Chicago's role in the development of neoliberalism. A companion in the true sense of the word, this volume surveys a wide body of Chicago economic studies and guides readers carefully through each. The Companion offers biographies of leading Chicago economists and evaluations of the School's connection to approaches to economics that draw from and complement the School, including the Virginia School and the work of Armen Alchian and Edward Lazear. Moreover, this book is a first in many respects as it analyzes the interconnections of the Chicago School's theory, methodology, and policy, and considers by what means and ideas the School's policy framework is driven. The breadth and depth of the insights presented here will appeal especially to students and scholars of economics and historians interested in economics, social science and applied public policy.


Theory and Practice, Third Edition

Author: Douglas R. Stinson

Publisher: CRC Press

ISBN: 1420057138

Category: Computers

Page: 616

View: 8861

THE LEGACY... First introduced in 1995, Cryptography: Theory and Practice garnered enormous praise and popularity, and soon became the standard textbook for cryptography courses around the world. The second edition was equally embraced, and enjoys status as a perennial bestseller. Now in its third edition, this authoritative text continues to provide a solid foundation for future breakthroughs in cryptography. WHY A THIRD EDITION? The art and science of cryptography has been evolving for thousands of years. Now, with unprecedented amounts of information circling the globe, we must be prepared to face new threats and employ new encryption schemes on an ongoing basis. This edition updates relevant chapters with the latest advances and includes seven additional chapters covering: Pseudorandom bit generation in cryptography Entity authentication, including schemes built from primitives and special purpose "zero-knowledge" schemes Key establishment including key distribution and protocols for key agreement, both with a greater emphasis on security models and proofs Public key infrastructure, including identity-based cryptography Secret sharing schemes Multicast security, including broadcast encryption and copyright protection THE RESULT... Providing mathematical background in a "just-in-time" fashion, informal descriptions of cryptosystems along with more precise pseudocode, and a host of numerical examples and exercises, Cryptography: Theory and Practice, Third Edition offers comprehensive, in-depth treatment of the methods and protocols that are vital to safeguarding the mind-boggling amount of information circulating around the world.

Parameter Estimation and Inverse Problems

Author: Richard C. Aster,Brian Borchers,Clifford H. Thurber

Publisher: Academic Press

ISBN: 0123850495

Category: Science

Page: 376

View: 3160

Parameter Estimation and Inverse Problems, Second Edition provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory. The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors’ treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics. Parameter Estimation and Inverse Problems, Second Edition introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems. The textbook includes Appendices covering essential linear algebra, statistics, and notation in the context of the subject. Includes appendices for review of needed concepts in linear, statistics, and vector calculus. Accessible to students and professionals without a highly specialized mathematical background.

Radar Systems Analysis and Design Using MATLAB Third Edition

Author: Bassem R. Mahafza

Publisher: CRC Press

ISBN: 143988496X

Category: Business & Economics

Page: 772

View: 5062

Developed from the author’s graduate-level courses, the first edition of this book filled the need for a comprehensive, self-contained, and hands-on treatment of radar systems analysis and design. It quickly became a bestseller and was widely adopted by many professors. The second edition built on this successful format by rearranging and updating topics and code. Reorganized, expanded, and updated, Radar Systems Analysis and Design Using MATLAB®, Third Edition continues to help graduate students and engineers understand the many issues involved in radar systems design and analysis. Each chapter includes the mathematical and analytical coverage necessary for obtaining a solid understanding of radar theory. Additionally, MATLAB functions/programs in each chapter further enhance comprehension of the theory and provide a source for establishing radar system design requirements. Incorporating feedback from professors and practicing engineers, the third edition of this bestselling text reflects the state of the art in the field and restructures the material to be more convenient for course use. It includes several new topics and many new end-of-chapter problems. This edition also takes advantage of the new features in the latest version of MATLAB. Updated MATLAB code is available for download on the book’s CRC Press web page.

Sports Biomechanics

Reducing Injury Risk and Improving Sports Performance

Author: Roger Bartlett,Melanie Bussey

Publisher: Routledge

ISBN: 1135282269

Category: Medical

Page: 360

View: 852

When working with sports men and women, the biomechanist is faced with two apparently incompatible goals: reducing injury risk and improving sports performance. Now in a fully updated and revised edition, Sports Biomechanics introduces the fundamental principles that underpin our understanding of the biomechanics of both sports injury and performance, and explains how contemporary biomechanical science can be used to meet both of those goals simultaneously. The first four chapters of this book look closely at sports injury, including topics such as the properties of biological materials, mechanisms of injury occurrence, risk reduction, and the estimation of forces in biological structures. The last four chapters concentrate on the biomechanical enhancement of sports performance including analytical techniques, statistical and mathematical modelling of sports movements, and the use of feedback to enhance sports performance. Drawing on the very latest empirical and epidemiological data, and including clear concise summaries, self test questions and guides to further reading in every chapter, this book is essential reading for all advanced undergraduate and postgraduate students with an interest in biomechanics, sports injury, sports medicine, physical therapy or performance analysis. Visit the companion website at www.routledge.com/cw/bartlett

Foundations of Abstract Analysis

Author: Jewgeni H. Dshalalow

Publisher: Springer Science & Business Media

ISBN: 1461459621

Category: Mathematics

Page: 748

View: 8220

Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presented in a self-contained way suitable both for classroom use and for self-study. While this book carries the rigor of advanced modern analysis texts, it elaborates the material in much greater details and therefore fills a gap between introductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of the potential overload of new words, definitions, and concepts, the book (in its unique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded by informal discussions and blueprints followed by thorough details and supported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of the book, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. Prerequisites include advanced calculus, linear algebra, complex variables, and calculus based probability.

Petroleum Production Engineering, A Computer-Assisted Approach

Author: Boyun Guo,

Publisher: Elsevier

ISBN: 9780080479958

Category: Technology & Engineering

Page: 312

View: 6779

Petroleum Production Engineering, A Computer-Assisted Approach provides handy guidelines to designing, analyzing and optimizing petroleum production systems. Broken into four parts, this book covers the full scope of petroleum production engineering, featuring stepwise calculations and computer-based spreadsheet programs. Part one contains discussions of petroleum production engineering fundamentals, empirical models for production decline analysis, and the performance of oil and natural gas wells. Part two presents principles of designing and selecting the main components of petroleum production systems including: well tubing, separation and dehydration systems, liquid pumps, gas compressors, and pipelines for oil and gas transportation. Part three introduces artificial lift methods, including sucker rod pumping systems, gas lift technology, electrical submersible pumps and other artificial lift systems. Part four is comprised of production enhancement techniques including, identifying well problems, designing acidizing jobs, guidelines to hydraulic fracturing and job evaluation techniques, and production optimization techniques. *Provides complete coverage of the latest techniques used for designing and analyzing petroleum production systems *Increases efficiency and addresses common problems by utilizing the computer-based solutions discussed within the book * Presents principles of designing and selecting the main components of petroleum production systems

The Princeton Companion to Mathematics

Author: Timothy Gowers,June Barrow-Green,Imre Leader

Publisher: Princeton University Press

ISBN: 9781400830398

Category: Mathematics

Page: 1056

View: 9654

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors incude: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger

Advanced Real Analysis

Author: Anthony W. Knapp

Publisher: Springer Science & Business Media

ISBN: 9780817644420

Category: Mathematics

Page: 466

View: 912

* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

Elementary Analysis

The Commonwealth and International Library: Mathematics Division

Author: K. S. Snell,J. B. Morgan

Publisher: Elsevier

ISBN: 1483137082

Category: Mathematics

Page: 248

View: 8070

Elementary Analysis, Volume 1 introduces the reader to elementary analysis in an informal manner and provides the practical experience in algebraic and analytic operations to lay a sound foundation of basic skills. The preliminary ideas are illustrated by applications to the simpler algebraic functions. Emphasis is on fundamental principles, rather than manipulative techniques. This volume is comprised of 14 chapters and begins with a discussion on number systems, covering concepts ranging from number scales to rational and real numbers, binary operations, and deductive methods. The following chapters deal with sets, vectors and congruences, and functions. Exponential and logarithmic functions, the straight line, and linear function are also considered. The remaining chapters focus on the quadratic function; the principle of mathematical induction and its applications; differentiation and the inverse process; and integration and its applications. Differential equations are presented, along with the definite integral. This book will be of particular value to teachers and students in training colleges.