Hypersurface Theory in the Resolution of Differential Equations

This body of work is fundamentally intended to be an interface between tertiary mathematical studies and advanced research in diverse related areas. The author hopes to draw the attention of the reader to possible oversights of researchers attempting to examine and resolve the most common of ordinary and partial differential equations. Being that the text serves the purpose of a doctorate dissertation, it does not quite exhaustively develop any aspect of its content. However, the unique combination of pertinent subtopics gels into a coherent academic array with applicable seeds of creativity to be further elucidated by readers in touch with the content. Both computational and theoretical exercises abound. In the end, this piece is expected to develop into a prolific study companion for many.