Caption: Course Catalog - 1888-1889
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46 UNIVERSITY OF ILLINOIS. Those who make further preparation than that required before entering can make their course more extensive and profitable. The following suggestions are offered to such as wish to make thorough work : Either French or German are studied during two years: some preparation in Latin will be of great assistance in these languages. The engineer and architect shonld be adepts in the various departments of drawing, and some previous study of this branch will be of great advantage. Warren's Draughting Instruments may be used as a text book, and the drawings made on smooth paper, eight by ten inches. STUDIES PURSUED BY ALL ENGINEERING STUDENTS. The subjects common to all the schools in the College of engineering will be described first; the topics peculiar to each will be noticed under their specific names. PURE MATHEMATICS, FIRST TEAR. Trigonometry.— Plain and spherical. Fundamental relations between trigonometrical functions of angles or arcs; construction and use of tables ; solution of triangles ; projection of spherical triangles ; angles as functions of sides and sides as functions of angles ; general formulas ; applications. Analytical Geometry.—The point and right line in a plane ; conic sections, their equations and properties ; the tangent and subtangent; normal and subnormal, pole and polar, supplementary chords, conjugate diameters, etc. Discussion of the general equation of the second degree containing two variables. Advanced Algebra.—Functions and their notation ; series and the theories of limits ; imaginary quantities ; general theory of equations. PURE MATHEMATICS, SECOND TEAR. 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.
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