Repository: UIHistories Project: Course Catalog - 1899-1900 [PAGE 232]

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23°

GENERAL DESCRIPTION OF COURSES

taken with course 2 in advanced algebra. /.; Tu., Th.; section A, i;

section B, 2; section C, 3; section D, 4; section E, 6; (2). Associate

Professor TOWNSEND, Mr. MILNE, Mr. COAR, and Mr. SHORT.

6. ANALYTICAL GEOMETRY.—The aim is to acquaint the student

with analytical methods of investigation and to familiarize him with some of the most recent developments in synthetic geometry; to make him more skillful in the use of algebraic processes, especially as a means of demonstrating geometric properties of loci. Subjects considered are the elementary theory of the point and right line in a plane; use of abbreviated notation; elementary theory of the conic sections, their equations and properties developed analytically; poles and polars; synthetic geometry of the circle, and the discussion of the general equation of the second degree, and of some higher plane curves. The course will also include a discussion of the following subjects: Coordinate systems for a point in space, the locus in space of an equation of the first and second degree, planes and straight lines, quadratic surfaces. Tanner and Allen's Analytic Geometry. II.; daily; section A, 1; section B, 3; section C, 6; (5). Associate

Professor TOWNSEND, Mr. MILNE, Mr. COAR, and Mr. SHORT.

Required: Mathematics 2, 4 or 1, 3. 7. DIFFERENTIAL CALCULUS.—Variables and functions; limits and infinitesimals; differentials and derivatives; differentiation of explicit functions, implicit functions, and functions of several variables ; derivatives of higher orders; successive derivatives, developments in series; maxima and minima of functions; indeterminate forms; plane curves, tangents, and normals; asymptotes, singular points, and curve tracing; theory of envelopes, of curvature, of evoIutes, and of involutes. Byerly's Differential Calculus. I.; daily; section A, 1; section B, 2; section C, 4; (5). Professor SHATTUCK

and Mr. SHORT.

Required: Mathematics 6. 9. INTEGRAL CALCULUS.—Elementary forms of integrations; integrals immediately reducible to the elementary forms; integration by rational transformations; integration of irrational algebraic differentials ; integration of transcendent functions; definite integrals; successive integration; differentiation under the sign of integration; integration by means of differentiating known integrals; double integrals; triple and multiple integrals; product of two definite integrals. Rectification and quadrature; the parabola, the ellipse, the cycloid, the Archimedean spiral, the logarithmic spiral, the limniscate,