Buy Continuous Functions of Vector Variables - Bookswagon
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Functional analysis and transforms > Continuous Functions of Vector Variables
36%
Continuous Functions of Vector Variables

Continuous Functions of Vector Variables


     0     
5
4
3
2
1



Available


X
About the Book

This text is an axiomatic treatment of the properties of continuous multivariable functions and related results from topology. Viewing multiple real variables as members of vector spaces, A. Guzman covers boundedness, extreme values and uniform continuity of functions, along with the connections between continuity and topological concepts such as connectedness and compactness. Suitable for advanced undergraduates preparing for graduate programmes in pure mathematics, the required background includes a course in the theory of single-variable calculus and the elements of linear algebra. The order of topics deliberately mimics the order of development in elementary calculus. This sequencing allows an elementary approach, with analogies to and generalizations from such familiar ideas as the Pythagorean theorem. The reader is frequently reminded that the pictures suggested by geometry are powerful guides and tools. The definition-theorem-proof format resides with an informal exposition, containing numerous historical comments and questions within and between the proofs. The objective is to present precise proofs, but in a structure and tone that teach the student to plan and write proofs, both in general and specifically for the real analysis course that the book anticipates will follow this one. Applications are included where they provide interesting illustrations of the principles and theorems presented. Problems, solutions, bibliography and index complete this book.

Table of Contents:
1 Euclidean Space.- 1.1 Multiple Variables.- 1.2 Points and Lines in a Vector Space.- 1.3 Inner Products and the Geometry of Rn.- 1.4 Norms and the Definition of Euclidean Space.- 1.5 Metrics.- 1.6 Infinite-Dimensional Spaces.- 2 Sequences in Normed Spaces.- 2.1 Neighborhoods in a Normed Space.- 2.2 Sequences and Convergence.- 2.3 Convergence in Euclidean Space.- 2.4 Convergence in an Infinite-Dimensional Space.- 3 Limits and Continuity in Normed Spaces.- 3.1 Vector-Valued Functions in Euclidean Space.- 3.2 Limits of Functions in Normed Spaces.- 3.3 Finite Limits.- 3.4 Continuity.- 3.5 Continuity in Infinite-Dimensional Spaces.- 4 Characteristics of Continuous Functions.- 4.1 Continuous Functions on Boxes in Euclidean Space.- 4.2 Continuous Functions on Bounded Closed Subsets of Euclidean Space.- 4.3 Extreme Values and Sequentially Compact Sets.- 4.4 Continuous Functions and Open Sets.- 4.5 Continuous Functions on Connected Sets.- 4.6 Finite-Dimensional Subspaces of Normed Linear Spaces.- 5 Topology in Normed Spaces.- 5.1 Connected Sets.- 5.2 Open Sets.- 5.3 Closed Sets.- 5.4 Interior, Boundary, and Closure.- 5.5 Compact Sets.- 5.6 Compactness in Infinite Dimensions.- Solutions to Exercises.- References.

Review :
"The book is devoted to mathematical analysis in multi-dimensional spaces, including infinite-dimensional ones!One of the important characteristics of the text is the topological approach. !It is worth mentioning that all these ideas are presented in conformity with the situation, i.e. they are strictly related to normed spaces and no unnecessary abstract setting is used. ! The language is very clear and sometimes very 'fresh' if compared with classical textbooks, so that it may better appeal to the reader. There are many exercises, and the book concludes with a chapter containing solutions." --MATHEMATICAL REVIEWS "This is a textbook on calculus of several variables. It covers algebraic and metric structure of the Euclidean space, convergence, basic properties of continuous functions and topology in normed spaces... In my opinion, this topological approach is one of the advantages of the book under review. It is written very clearly and contains numerous examples and instructive pictures. Each section is endowed with a set of exercises, and the book is concluded with solutions to these exercises. This is a nice and user-friendly textbook which can be recommended for a one-semester course in multivariable calculus." --ZENTRALBLATT MATH "The presentation is detailed and clear. The leisurely discursive style adopted by the author will be appreciated by beginners. The fact that the solution of each and every exercise can be found at the end of the book, considerable enhances its value and makes it suitable also for individual study. This book successfully bridges the gap between elemntary calculus and such higher disciplines as real functions, general topology, and, in particular, functional analysis." --PUBLICATIONES MATHEMATICAE, DEBRECEN


Best Sellers


Product Details
  • ISBN-13: 9780817642730
  • Publisher: Birkhauser Boston
  • Publisher Imprint: Birkhauser Boston
  • Height: 235 mm
  • No of Pages: 210
  • Returnable: Y
  • ISBN-10: 0817642730
  • Publisher Date: 31 Jul 2002
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Width: 155 mm


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Continuous Functions of Vector Variables
Birkhauser Boston -
Continuous Functions of Vector Variables
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Continuous Functions of Vector Variables

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    Fresh on the Shelf


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!