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Full-Text Articles in Physical Sciences and Mathematics
A Topological Approach To Nonlinear Analysis, Wendy Ann Peske
A Topological Approach To Nonlinear Analysis, Wendy Ann Peske
Theses Digitization Project
A topological approach to nonlinear analysis allows for strikingly beautiful proofs and simplified calculations. This topological approach employs many of the ideas of continuous topology, including convergence, compactness, metrization, complete metric spaces, uniform spaces and function spaces. This thesis illustrates using the topological approach in proving the Cauchy-Peano Existence theorem. The topological proof utilizes the ideas of complete metric spaces, Ascoli-Arzela theorem, topological properties in Euclidean n-space and normed linear spaces, and the extension of Brouwer's fixed point theorem to Schauder's fixed point theorem, and Picard's theorem.
Math, Music, And Membranes: A Historical Survey Of The Question "Can One Hear The Shape Of A Drum"?, Tricia Dawn Mccorkle
Math, Music, And Membranes: A Historical Survey Of The Question "Can One Hear The Shape Of A Drum"?, Tricia Dawn Mccorkle
Theses Digitization Project
In 1966 Mark Kac posed an interesting question regarding vibrating membranes and the sounds they make. His article entitled "Can One Hear the Shape of a Drum?", which appeared in The American Mathematical Monthly, generated much interest and scholarly debate. The evolution of Kac's intriguing question will be the subject of this project.