An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of, by the Rev. M. O'Brien.

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SUMMARY.

CHAP. XII.
Differentiation, 8yc. of Functions of two or more independent Variables.
ARTICLE PAGE
256. General Introduction and Notation..................... 370
259. Given u =f (x, y), to find the developement of
u' =f(x+h, y y+k),
h and k being any two indeterminate magnitudes........ 373
263. To find the successive differentials of a function of two
variables expressed generally by u =f(x, y)............ 380
269. To find the developement of a function u' of three variables
x, y, z independent of each other, corresponding to their
values x + h, y + k, z + I respectively................. 385
276. Elimination of constant quantities, and of functions whose
forms are indeterminate................................ 393
281. Lagrange's Theorem, and its Applications................ 399
282. Laplace's Theorem................................... 412
CHAP. XIII.
Maxima and Minima of Functions of two or more independent Variables.
283. To investigate the conditions necessary that u = (f(x, y)
may be a maximum or a minimum, and to find a criterion
for deciding whether it is a maximum or a minimum..... 415
286. To investigate the conditions necessary that a function of
three variables may be a maximum or a minimum, and to
deduce a criterion for deciding which it is............... 424
CHAP. XIV.
Tangents, 4c. to Curve Surfaces and Curves of Double Curvature.
290. General Introduction to the subject..................... 428
291. To find the equation to a plane, touching a given surface
at any assigned point.................................. 429
294. Of all the straight lines that can be drawn from the point
of contact in the tangent plane, to find that which is inclined to the plane of xy at the greatest angle............. 434
296. To find the equations to the normal of a curve surface at
any proposed point.............................. 436