Repository: UIHistories Project: Course Catalog - 1877-1878 Version B [PAGE 27]

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College of Engineering.

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Transversals; Harmonic Proportions, etc. Trigonometry.—Analytical and Plane. Relations between ,the functions of an arc; Formation and use of Tables; Solution of plane triangles. Analitical Geometry.—Construction of equations; Discussion, in a plane, of the point, right-line, circle, ellipse, parabola and hyperbola; Higher plane curves, cycloid, cissoid of Diodes, etc.— 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. Analytical Geomtry.—Loci in space; Surfaces of the second order. Differential Calculus.—Differentials 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.

PHYSICS.

The course in Physics is complete and thorough, embracing the four kinds of work following : 1. Recitation, four exercises a week, in which a text book is used as a guide. 2. Physical experiments one day each week, in which the student uses the instruments in testing the principles taught. 3. Illustrated experiments one evening each week, in which the more costly apparatus is used before the whole class, in such experiments as are difficult to perform, and which are most effective when prepared for an audience. 4. The higher physical experiments by advanced classes, consisting either of researches, or of reviews of careful and elaborate experiments previously worked up by others. To prepare for the last named work, the student must have pursued Physical studies at least one term in the first three. The department of Physics is amply provided with illustrative