Military schools and courses of instruction in the science and art of war, / in France, Prussia, Austria, Russia, Sweden, Switzerland, Sardinia, England, and the United States. Drawn from recent official reports and documents. Revised Edition

by Unknown

Lessons 14–18. Analytical Applications of the Differential Calculus.

Development of F(x + h,) according to ascending powers of h. Limits within which the remainder is confined on stopping at any assigned power of h.

Development of F(x,) according to powers of x or x - a; a being a quantity arbitrarily assumed. Application to the functions sin(x,) cos x, a^x, (1 + x^m) and log.(1 + x.) Numerical applications. Representation of cos x and sin x by imaginary exponential quantities.

Developments of cos^m x and sin^m x in terms of sines and curves of multiples of x.

Development of F(x + h, y + k,) according to powers of h and k. Development of F(x, y) according to powers of x and y. Expression for the remainder. Theorem on homogeneous functions.

Maxima and minima of functions of a single variable; of functions of several variables, whether independent or connected by given equations. How to discriminate between maxima and minima values in the case of one and two independent variables.

True values of functions, which upon a particular supposition assume one or another of the forms

00, ∞∞, ∞ + 0, 0⁰, 4^∞

Lessons 19–23. Geometrical Applications. Curvature of Plane Curves.

Definition of the curvature of a plane curve at any point. Circle of curvature. Center of curvature. This center is the point where two infinitely near normals meet.