UIHistories Project: A History of the University of Illinois by Kalev Leetaru
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Repository: UIHistories Project: Course Catalog - 1895-1896 [PAGE 180]

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180

GENERAL DESCRIPTION OF COURSES

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 skilful 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. Wood's Coordinate Geometry. Spring term, full study. Mr. BUBNHAM. Required: Math. 2, 4. 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 evolutes, and involutes. Byerly 's Differential Calculus. Fall term, full study. Professor

SHATTUCK.

Required: Math. 2, 4, 6.

8. ADVANCED ANALYTICAL GEOMETRY.—Position and di-

rection in space ; direction and angles ; projections of lines, direction cosines ; transformation of coordinates ; the general and normal equations of the plane ; also in terms of the intercepts ; the plane satisfying given conditions ; relations of planes to one another ; perpendicular distance to a plane ; bisectors of dihedral angles; symmetrical equations of a straight line ; condition that a line shall be parallel to a plane ; equation of the common perpendicular to two given lines; condition of intersection ; a quadric surface ; conjugate axes and planes ; classes of quadrics ; tangent and polar lines, and planes to a quadric ; surfaces derived from generating curves ; the equations of the helix ; the conoid. Wood''s Coordinate Geometry. Winter term, full study. Professor SHATTUCK. Required: Math. 2, 4, 6, 7. 9. INTEGRAL CALCULUS.—Elementary forms of integration ; integrals immediately reducible to the elementary forms;