UIHistories Project: A History of the University of Illinois by Kalev Leetaru
N A V I G A T I O N D I G I T A L L I B R A R Y

## Repository: UIHistories Project: Board of Trustees Minutes - 1878 [PAGE 136]

Caption: Board of Trustees Minutes - 1878
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136

Simultaneously with this practice, the designing of such machine elements as pullies, journal boxes, cranks, stuffing boxes, etc., cultivates a knowledge of proportion, and of its proper representation on paper. This practice in designing and drawing is a leading feature in the course of instruction. This elementary practice lits the student for the advanced shop practice in designing and construction of complete machines undertaken later in the course.

STUDIES.

The studies are given by the year and term in the tabular view of the course. The order of studies there indicated should be closely followed, that the student may avoid interference of his hours of recitation. The following is a detailed view :

PUKE MATHEMATICS.

Advanced Geometry.—Applications of algebra to geometry; transversals ; harmonic proportions, etc. Trigonometry.—Analytical and plane; relations between the functions of an arc ; formation and use of tables ; solution of plane triangles. Analytical Geometry.—Construction of equations ; discussion, in a plane, of the point, right-line, circle, ellipse, parabola and hyperbola ; higher plane curves, cycloid, cissiod of diodes, et*c. Differential Calculus.—Differentials of algebraic and transcendental functions; Maclaurin's Theorem; Taylor's Theorem; maxima and minima of functions of one variable ; equations of tangents, normals, sub-tangents, sub-normals, etc.; differentials of lines, surfaces and volumes. Integral Calculus.—Integration of elementary forms and of rational fractions ; rectification of plane curves; quadrature of plane areas and surfaces of revolution ; and cubature of solids of revolution.

SECOND YEAR.

Advanced Algebra.—Binomial theorem ; properties and summation of series. Exponential quantities, Logarithms. General theory and methods of solving equations. Ajialytical Geometry.—Loci in space, surfaces of the second order. Differential Calculus.—Differential and maxima and minima of functions of two or more variables ; osculatory curves; radius of curvature; evolutes, involutes and envelopes ; discussion of algebraic and transcendental curves and surfaces ; tangent and normal planes ; partial differentials of surfaces and volumes. Integral Calculus.—Integration of transcendental and irrational differentials ; differentials of higher orders ; differential equations ; rectifications, quadrature and cubature in general. Spherical Trigonometry.—General formulas; solution of spherical triangles. Calculus of Variations will be taught to advanced students.