*A Problem-oriented Approach*

Author: V. K. Krishnan

Publisher: PHI Learning Pvt. Ltd.

ISBN: 9788120316270

Category: Functional analysis

Page: 404

View: 3376

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## Textbook of Functional Analysis

## TEXTBOOK OF FUNCTIONAL ANALYSIS

This unique, comprehensive and student-friendly book, now in its second edition, continues to hold the purpose of explaining and illustrating the use of the basic theorems in functional analysis through solved numerical problems. The text has been revised on the basis of the readers’ feedback. The book now covers ample worked-out numerical problems related to the spectral properties of compact operators on Banach spaces as well as on Hilbert spaces. Inclusion of a few problems based on the square root of a positive operator also contributes to the major highlights of this edition. Such a practical approach will greatly facilitate students to have a thorough grasp of the subject. This stands in stark contrast to the method followed in most of the books where a great amount of theory is given with a smattering of problems to elucidate the topics discussed. Intended as a text for the students pursuing postgraduate courses in mathematics, this book with its systematic and precise presentation and provision of a large number of exercises should prove to be a trendsetter in its approach to the subject. This novelty of approach appeals the students in particular.
## Functional Analysis, Calculus of Variations and Optimal Control

Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.
## Practical Software Testing

Based on the needs of the educational community, and the software professional, this book takes a unique approach to teaching software testing. It introduces testing concepts that are managerial, technical, and process oriented, using the Testing Maturity Model (TMM) as a guiding framework. The TMM levels and goals support a structured presentation of fundamental and advanced test-related concepts to the reader. In this context, the interrelationships between theoretical, technical, and managerial concepts become more apparent. In addition, relationships between the testing process, maturity goals, and such key players as managers, testers and client groups are introduced. Topics and features: - Process/engineering-oriented text - Promotes the growth and value of software testing as a profession - Introduces both technical and managerial aspects of testing in a clear and precise style - Uses the TMM framework to introduce testing concepts in a systemmatic, evolutionary way to faciliate understanding - Describes the role of testing tools and measurements, and how to integrate them into the testing process Graduate students and industry professionals will benefit from the book, which is designed for a graduate course in software testing, software quality assurance, or software validation and verification Moreover, the number of universities with graduate courses that cover this material will grow, given the evoluation in software development as an engineering discipline and the creation of degree programs in software engineering.
## A Companion to Analysis

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 First Course in Functional Analysis

Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside real applications in analysis. The background required for a student taking this course is minimal; basic linear algebra, calculus up to Riemann integration, and some acquaintance with topological and metric spaces.
## Quantitative Finance

Quantitative Finance: An Object-Oriented Approach in C++ provides readers with a foundation in the key methods and models of quantitative finance. Keeping the material as self-contained as possible, the author introduces computational finance with a focus on practical implementation in C++. Through an approach based on C++ classes and templates, the text highlights the basic principles common to various methods and models while the algorithmic implementation guides readers to a more thorough, hands-on understanding. By moving beyond a purely theoretical treatment to the actual implementation of the models using C++, readers greatly enhance their career opportunities in the field. The book also helps readers implement models in a trading or research environment. It presents recipes and extensible code building blocks for some of the most widespread methods in risk management and option pricing. Web Resource The author’s website provides fully functional C++ code, including additional C++ source files and examples. Although the code is used to illustrate concepts (not as a finished software product), it nevertheless compiles, runs, and deals with full, rather than toy, problems. The website also includes a suite of practical exercises for each chapter covering a range of difficulty levels and problem complexity.
## Requirements Analysis

Written clearly, without jargon, for an audience of people who do not necessarily know any of the techniques before picking up the book, this is a compendium of the various analysis techniques that have developed over the last 30 years, organized in terms of an architectural framework.
## Functional Analysis, Sobolev Spaces and Partial Differential Equations

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
## RNA-seq Data Analysis

The State of the Art in Transcriptome Analysis RNA sequencing (RNA-seq) data offers unprecedented information about the transcriptome, but harnessing this information with bioinformatics tools is typically a bottleneck. RNA-seq Data Analysis: A Practical Approach enables researchers to examine differential expression at gene, exon, and transcript levels and to discover novel genes, transcripts, and whole transcriptomes. Balanced Coverage of Theory and Practice Each chapter starts with theoretical background, followed by descriptions of relevant analysis tools and practical examples. Accessible to both bioinformaticians and nonprogramming wet lab scientists, the examples illustrate the use of command-line tools, R, and other open source tools, such as the graphical Chipster software. The Tools and Methods to Get Started in Your Lab Taking readers through the whole data analysis workflow, this self-contained guide provides a detailed overview of the main RNA-seq data analysis methods and explains how to use them in practice. It is suitable for researchers from a wide variety of backgrounds, including biology, medicine, genetics, and computer science. The book can also be used in a graduate or advanced undergraduate course.
## Problem-Solving Through Problems

This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.
## Programming and Problem Solving with C++: Comprehensive

A Reorganized and Updated Edition of the Bestselling, Definitive C++ Text The bestselling Programming and Problem Solving with C++ is the single clearest and most comprehensive introduction to C++, object-oriented programming, and software development on the market. Accessible enough for beginning students, this text has been accepted by hundreds of colleges and universities around the world as a model text for the ACM/IEEE-recommended curricula for CS1 courses and for the Advanced Placement exam in computer science. Renowned author team Nell Dale and Chip Weems’s student-centered, pragmatic, and hands-on approach focuses on making even the most difficult concepts in computer science programming accessible to all students. Comprehensive and student-friendly, Programming and Problem Solving with C++, Sixth Edition remains the definitive text for introductory computer science programming courses. New and Key Features: - Contains new programming exercises and new, more student-friendly organization of material - Features strong pedagogical elements, including real-world case studies and highly relevant exercises that reinforce key concepts and build crucial skills - Introduces C++ language constructs in parallel with the appropriate theory so that students immediately realize practical applications - Every new printed copy of the text is packaged with full student access to Turing's Craft Custom CodeLab. Customized to match the organization of the text, CodeLab offers students hands-on C++ programming experience. The system immediately judges the correctness of code typed in by students, and offers hints for building and improving coding skills - Ideally suited for bundling with A Laboratory Course in C++ (978-1-284-02590-3), a digital resource prepared by Nell Dale - Includes a full suite of ancillary resources including a complete source code for students and instructors, PowerPoint Lecture Outlines, and a Test Bank
## The How and Why of One Variable Calculus

First course calculus texts have traditionally been either “engineering/science-oriented” with too little rigor, or have thrown students in the deep end with a rigorous analysis text. The How and Why of One Variable Calculus closes this gap in providing a rigorous treatment that takes an original and valuable approach between calculus and analysis. Logically organized and also very clear and user-friendly, it covers 6 main topics; real numbers, sequences, continuity, differentiation, integration, and series. It is primarily concerned with developing an understanding of the tools of calculus. The author presents numerous examples and exercises that illustrate how the techniques of calculus have universal application. The How and Why of One Variable Calculus presents an excellent text for a first course in calculus for students in the mathematical sciences, statistics and analytics, as well as a text for a bridge course between single and multi-variable calculus as well as between single variable calculus and upper level theory courses for math majors.
## Optimization by Vector Space Methods

Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
## Functional Analysis

The Book Is Intended To Serve As A Textbook For An Introductory Course In Functional Analysis For The Senior Undergraduate And Graduate Students. It Can Also Be Useful For The Senior Students Of Applied Mathematics, Statistics, Operations Research, Engineering And Theoretical Physics. The Text Starts With A Chapter On Preliminaries Discussing Basic Concepts And Results Which Would Be Taken For Granted Later In The Book. This Is Followed By Chapters On Normed And Banach Spaces, Bounded Linear Operators, Bounded Linear Functionals. The Concept And Specific Geometry Of Hilbert Spaces, Functionals And Operators On Hilbert Spaces And Introduction To Spectral Theory. An Appendix Has Been Given On Schauder Bases.The Salient Features Of The Book Are: * Presentation Of The Subject In A Natural Way * Description Of The Concepts With Justification * Clear And Precise Exposition Avoiding Pendantry * Various Examples And Counter Examples * Graded Problems Throughout Each ChapterNotes And Remarks Within The Text Enhances The Utility Of The Book For The Students.
## Introductory Functional Analysis with Applications

Market_Desc: · Undergraduate and Graduate Students in Mathematics and Physics· Engineering· Instructors
## Multimodality

This textbook provides the first foundational introduction to the practice of analysing multimodality, covering the full breadth of media and situations in which multimodality needs to be a concern. Readers learn via use cases how to approach any multimodal situation and to derive their own specifically tailored sets of methods for conducting and evaluating analyses. Extensive references and critical discussion of existing approaches from many disciplines and in each of the multimodal domains addressed are provided. The authors adopt a problem-oriented perspective throughout, showing how an appropriate foundation for understanding multimodality as a phenomenon can be used to derive strong methodological guidance for analysis as well as supporting the adoption and combination of appropriate theoretical tools. Theoretical positions found in the literature are consequently always related back to the purposes of analysis rather than being promoted as valuable in their own right. By these means the book establishes the necessary theoretical foundations to engage productively with today’s increasingly complex combinations of multimodal artefacts and performances of all kinds.
## Stroke Rehabilitation

Gillen's Stroke Rehabilitation: A Function-Based Approach, 3rd Edition is theonly comprehensive, evidence-based stroke rehabilitation resource for occupational therapists. Extensively updated with the latest research in assessment and intervention, this essential text presents a holistic, application-based approach that integrates background medical information, samples of functionally based evaluations, and current treatment techniques and intervention strategies to help you confidently manage the growing number of stroke rehabilitation clients. UNIQUE! Case studies challenge you to apply rehabilitation concepts to realistic scenarios. Evidence-based clinical trials and outcome studies clearly outline the basis for stroke interventions. UNIQUE! Survivor's Perspectives help you understand the stroke rehabilitation process from the client's point-of-view. UNIQUE! A multidisciplinary approach highlights discipline-specific distinctions in stroke rehabilitation among occupation and physical therapists, physicians, and speech-language pathologists. Review questions in each chapter help you assess your understanding of rehabilitation concepts. Key terms and chapter objectives at the beginning of each chapter help you study more efficiently. Three new chapters broaden your understanding of stroke intervention in the areas ofUsing Technology to Improve Limb Function, Managing Speech and Language Deficits after Stroke, andParenting after Stroke. Learning activities and interactive references on a companion Evolve Resources website help you review textbook content and locate additional information.
## Essential Bioinformatics

Essential Bioinformatics is a concise yet comprehensive textbook of bioinformatics, which provides a broad introduction to the entire field. Written specifically for a life science audience, the basics of bioinformatics are explained, followed by discussions of the state-of-the-art computational tools available to solve biological research problems. All key areas of bioinformatics are covered including biological databases, sequence alignment, genes and promoter prediction, molecular phylogenetics, structural bioinformatics, genomics and proteomics. The book emphasizes how computational methods work and compares the strengths and weaknesses of different methods. This balanced yet easily accessible text will be invaluable to students who do not have sophisticated computational backgrounds. Technical details of computational algorithms are explained with a minimum use of mathematical formulae; graphical illustrations are used in their place to aid understanding. The effective synthesis of existing literature as well as in-depth and up-to-date coverage of all key topics in bioinformatics make this an ideal textbook for all bioinformatics courses taken by life science students and for researchers wishing to develop their knowledge of bioinformatics to facilitate their own research.
## Miranda

This book introduces Miranda at a level appropriate for professionals with little or no prior experience in programming. The emphasis is on the process of crafting programs, solving problems, and avoiding common errors. Using a large number of running examples and case studies, the book encourages the design of well structured, reusable software together with proofs of correctness. A tear-out card enables readers to acquire a Miranda compiler from Research Software Ltd. at a substantial discount off the published list price.

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*A Problem-oriented Approach*

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Publisher: PHI Learning Pvt. Ltd.

ISBN: 9788120316270

Category: Functional analysis

Page: 404

View: 3376

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