The work here submitted to the notice of the public forms the third volume of a course intended to furnish to the mathematical student a pretty comprehensive view of the principles of modern analytical science. To complete this design will require a fourth volume in some measure supplementary to the three now completed and to contain the subject of Finite Differences a fuller inquiry into the theory of Partial Differential Equations and a chapter on Definite Integrals. This final volume I hope hereafter to be able to prepare although I do not propose to enter immediately upon the undertaking.
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