Commits
Comments (0)
Files changed (8)

+7 0.hgignore

+17 0AiryTreatise.sublimeproject

+0 0Original/An elementary treatise on partial differential equations  Sir George Biddell Airy.pdf

+28 0TeX/Master.tex

+13 0TeX/sections/chapter01.tex

+13 0TeX/sections/preface/airy.tex

+8 0TeX/sections/preface/current.tex

+14 0build.sh
Original/An elementary treatise on partial differential equations  Sir George Biddell Airy.pdf
Binary file added.
TeX/Master.tex
TeX/sections/chapter01.tex
+In all that follows, we shall suppose that it is always possible to effect simple integration; inasmuch as any difficulties of integration, connected with the solutions of partial differential equations, do not affect the principle of those solutions. Thus, for instance, we shall not hesitate to represent an unknown function of $x$ by $\chi''(x)$, (the second differentialcoefficient of $\chi(x)$), on the assumption that, whatever be the form of $\chi''(x)$, we can in some way find the function $\chi(x)$ of which it is the second differentialcoefficient.
+Before entering on the subject of Partial Differential Equations, it may be convenient to consider some of the characteristics of the solutions of Simple Differential Equations.
+To begin with Simple Differential Equations of the first order. Suppose, for facility of geometrical illustration, we consider the equation $y\frac{dy}{dx}=a$, or the equation $y\frac{dx}{dy}=b$, of which the former, translated geometrically, indicates that the subnormal of a planecurve (to be found) is constant, and the latter indicates that the subtangent is constant. The algebraical solutions are easily found: in each, there is a constant, and is not defined by it; a constant of that class described (perhaps improperly) by the term ``arbitrary,'' but which really means ``not yet determined, but enabling us by proper determination of its value so to fix the value of $x$ corresponding to a given value of $y$ that we can adjust the solution to some specific condition.''
TeX/sections/preface/airy.tex
+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 the important problems of Physical Science, which require for their complete investigation the aid of Partial Differential Equations.
TeX/sections/preface/current.tex
+This is a reproduction of George Biddell Airy's treatise for Cambridge University published in 1866. It has been recreated from the scans made available by Google\texttrademark.
+This work attempts to recreate the scanned work as faithfully as possible. Some changes have been made to the formatting, but the content remains the same. The source \LaTeX{} for this work is publicly available. If you find any errors, you may make the necessary corrections and contribute them back to the project.