Canonical Problems in Scattering and Potential Theory: Canonical Structures in Potential Theory

Hardcover (Print)
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $45.28
Usually ships in 1-2 business days
(Save 77%)
Other sellers (Hardcover)
  • All (10) from $45.28   
  • New (5) from $115.00   
  • Used (5) from $45.28   


Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified.

The first volume, Canonical Structures in Potential Theory, develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. The second volume, Acoustic and Electromagnetic Diffraction by Canonical Structures, examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction-the first complete description quantifying the scattering mechanisms in complex structures.

Read More Show Less

Editorial Reviews

Describes an analytical technique for determining diffraction from classes of canonical scatterers with edges and other complex cavity features. Develops the mathematics for solving mixed boundary value potential problems for structures with cavities and edges, and develops the theory of special functions, dual series, and functional analysis using transformations connected with Abel's integral equation to invert a singular part of the operator defining the potential. Chapter topics include electrostatic potential theory for open spherical and spheroidal shells, charged toroidal shells, and potential theory for conical structures with edges. Vinogradov is a scientist at the Institute of Radiophysics and Electronics in Ukraine. Annotation c. Book News, Inc., Portland, OR (
Read More Show Less

Product Details

Table of Contents

Mathematical Aspects of Potential Theory
Dual or Triple Series and Integral Equations
Electrostatic Potential Theory for Open Spherical Shells and Cavities
Open Spheroidal Conducting Shells and Cavities
Charged Toroidal Shells and Cavities
Potential Theory for Conical Structures with Edges
Two-Dimensional Potential Theory
Rigorous Solution Methods for more Complicated Structures

Mathematical Aspects of Wave Scattering
Acoustic Diffraction from a Circular Hole in a Thin Spherical Shell
Acoustic Diffraction from a Spherical Shell with Two Holes or an Equatorial Slot
Electromagnetic Diffraction from a Circular Hole in a Perfectly Conducting Spherical Shell
Electromagnetic Diffraction from a Spherical Shell with Two Circular Holes or an Equatorial Slot
Spherical Cavities with Dielectric Inclusions of Spherical Shape
Diffraction from Spheroidal Cavities
Applications of the Abel Integral Transform to Diffraction by Other Classes of Canonical Scatterers

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)