The work now offered to the University is strictly an Elementary Treatise. No attempt has been made to go
into all the varied details, of methods and examples, which present themselves in the wide field of Partial
Differential Equations, considered purely as an Algebraical subject. I have endeavoured, however, to omit no important consideration affecting the Principles of those Equations. And I trust that the methods of solution here explained, and the instances exhibited, will be found sufficient for application to nearly all those important problems of Physical Science, which require for their complete investigation the aid of Partial Differential Equations.