Repository: UIHistories Project: Course Catalog - 1871-1872 [PAGE 61]

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DEPARTMENTS.

59

science; nature of moral obligation; moral feeling; the Right; the Good. Practical ethics; Duties. Formation of character. Logic, formal and inductive (two lectures a week, alternating with Moral philosophy). Third Term.—History of Philosophy. Ancient schools of philosophy ; Scholasticism ; Modern schools of philosophy ; Influence of philosophy on the progress of civilization, and on modern sciences and arts. Inductive logic.

PURE

MATHEMATICS.

The studies in this Department are as follows: FIRST YEAR.— Geometry,—elementary principles, circle and measurement of angles, measurement and properties of polygons and the area of the circle, planes, polyedral angles, the prism, pyramid, cone and sphere, area of a spherical polygon of a lune, measurement of spherical angles. Higher Algebra,—formation of powers binomial theorem, extraction of root3 of any degree, radicals of any degree, properties and summation of series, exponantial quantities, logarithms, general theory of equations. Trigonometry,—plane, spherical and analytical, formation and use of tables, solution of right angled and oblique angled triangles, relation between the circular functions of any arc. •SECOND YEAR Analytical Geometry; geometrical construction; point and right line on a plane ; properties and measurement of the circle, ellipse, parabola and hyperbola; higher plane curves; the cycloid, cissoid of diocles, etc. Differential Calculus; differentials of algebraic functions of a single variable; Maclauren's Theorem ; Taylor's Theorem ; differentials of transcendental functions ; maxima and minima of functions of a single variable ; equations of tangent and normal; expressions for sub-tangent, sub-normal, etc.; differentials of an arc, plane area, surface and volume of revolution. Integral Calculus ; integration of monomials of particular binomials of rational fractions ; applications in the rectification and quadrature of curves, in the quadrature of surfaces of revolution, and in the cubature of volumes of revolution. THIRD YEAR.—Analytical Geometry; curves in space; discussion of the surfaces of the second order. Differential Calculus ; differentials of functions of two or more variables; maxima and minima of functions of. two or more variables; tendency of curves to coincide ; oscillatory curves; rndius of curvature; evolutes and involutes; envelopes; construction and discussion of algebraic curves, the logarithmic curve, the cycloid, spirals; general surfaces; equations of a tangent plane and a normal line ; partial differentials of a surface and of a volume. Integral Calculus ; integration of the differentials of circular functions and of circular arcs ; of certain irrational differentials ; of differentials containing transcendental quantities ; of the differentials of the higher orders and of differential equations ; rectification and quadrature of curves ; cubature of volumes in general. Calculus of Variations. Method of Least Squares.