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Caption: Course Catalog - 1891-1892
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44 UNIVERSITY OP ILLINOIS. 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. Written work in plotting and discussing loci from their equations is required from time to time. Newcomb's Analytic Geometry. Spring term, 5 hours a week. Professor MYEBS. Required: Math., 2, 4. 7. Differential Calculus.—Rules for the differentiation of functions of a single variable; successive differentiation ; development of functions ; maxima and minima of functions of a single variable ; differentials of an arc, plane area, surface and volume of revolution; elementary discussion of higher plane curves; the spirals, logarithmic curve, trochoid, etc.; algebraic curves. Integral Calculus. Integration of elementary forms and rational fractions; rectification of plane curves; quadrature of plane areas and surfaces of revolution; cubature of solids of revolution. Advanced Analytical Geometry. Loci in space; in point, right line, plane and surfaces of the second order. Advanced Calculus. Development of the second state of functions of any number of variables; differential equations; maxima and minima of functions of two or more variables ; construction and discussion of curves and surfaces ; integration of irrational and transcendental differentials and of differential equations of the higher orders and degree; applications; elements of elliptic integrals. Byerly's Differential Calculus; Byerly's Integral Calculus; Newcomb's Analytic Geometry. Fall, winter, and spring terms, 5 hours a week. Professor SHATTUCK. Required: Math., 2, 4, 5, 6.
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