In this dissertation the author investigates some triple trigonometric series which occur in the solution of mixed boundary value problems in elasticity and potential theory. By choosing a suitable integral representation for the sequence of unknown constants, the problem is reduced to solving a singular integral equation of the first kind. Twenty four cases in which the integral equation can be solved in closed form are discussed in detail.
In later chapters, the application of triple trigonometric series to problems in physics and engineering is demonstrated and closed form solutions for the physical parameters of interest are obtained.
","abstract_html":"<p>In this dissertation the author investigates some triple trigonometric series which occur in the solution of mixed boundary value problems in elasticity and potential theory. By choosing a suitable integral representation for the sequence of unknown constants, the problem is reduced to solving a singular integral equation of the first kind. Twenty four cases in which the integral equation can be solved in closed form are discussed in detail.</p> <p>In later chapters, the application of triple trigonometric series to problems in physics and engineering is demonstrated and closed form solutions for the physical parameters of interest are obtained.</p>","abstract_has_math":false,"creators":["Melrose, Gordon"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["John Tweed","John H. Heinbockel","James L. Cox, Jr."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1984,"date_issued":"1984-07-01T07:00:00Z","date_published":"1984-07-01T07:00:00Z","updated_at":"2026-07-24T03:35:15Z","subjects":["Trigonometric series","Boundary value problems","Elasticity","Mathematics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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In later chapters, the application of triple trigonometric series to problems in physics and engineering is demonstrated and closed form solutions for the physical parameters of interest are obtained.
"]},{"key":"dc:title","label":"Title","values":["Triple Trigonometric Series and Their Application to Mixed Boundary Value Problems"]}]}],"canonical_facts":{"dc:contributor":["John Tweed","John H. Heinbockel","James L. Cox, Jr."],"dc:creator":["Melrose, Gordon"],"dc:date.available":["2019-10-02T07:00:00Z"],"dc:description.abstract":["In this dissertation the author investigates some triple trigonometric series which occur in the solution of mixed boundary value problems in elasticity and potential theory. By choosing a suitable integral representation for the sequence of unknown constants, the problem is reduced to solving a singular integral equation of the first kind. Twenty four cases in which the integral equation can be solved in closed form are discussed in detail.
In later chapters, the application of triple trigonometric series to problems in physics and engineering is demonstrated and closed form solutions for the physical parameters of interest are obtained.
"],"dc:identifier":["https://digitalcommons.odu.edu/mathstat_etds/94"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Trigonometric series","Boundary value problems","Elasticity","Mathematics"],"dc:title":["Triple Trigonometric Series and Their Application to Mixed Boundary Value Problems"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:35:15Z"}