Repository: UIHistories Project: Course Catalog - 1894-1895 [PAGE 137]

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GENERAL LIST OP SUBJECTS.

137

plane satisfying given conditions; relations of planes to one another; perpendicular distance to a plane; bisectors of dihedral angles; symmetrical equations of a straight line ; condition that a line shall be parallel to a plane; equation of the common perpendicular to two given lines; condition of intersection ; a quadric surface ; conjugate axes and planes ; classes of quadrics ; tangent and polar lines, and planes to a quadric ; surfaces derived from generating curves ; the equations of the

helix; the conoid. NewcomVs Analytical Geometry. Winter term,

full study. Professor SHATTUCK. Required: Math. 2, 4, 6, 7. 9. INTEGRAL CALCULUS.—Elementary forms of integration; integrals immediately reducible to the elementary forms ; integration by rational transformations; integration of irrational algebraic differentials; integration of transcendent functions; definite integrals; successive integration ; differentiation under the sign of integration; integration by means of differentiating known integrals ; double integrals ; triple and multiple integrals; product of two definite integrals. Rectification and quadrature ; the parabola, the ellipse, the cycloid, the Archimedean spiral, the logarithmic spiral, the limniscate, the cycloid, quadrature of surfaces of revolution and of surfaces in general; cubature of volumes; the sphere, the pyramid, the ellipsoid, any solid of revolution, and of volumes in general. Niewcomb's Differential and Integral Calculus. Spring term, full study. Professor SHATTUCK. Required: Math. 2, 4, 6, 7, 8. 10. THEORY OF EQUATIONS.—The development of the general properties of equations; relations of the roots and the coefficients of an equation, with applications to symmetric functions; transformation of equations; solution of reciprocal and binomial equations; algebraic solution of cubics and biquadratics; properties of derived functions; the limits and separation of the roots of equations; the solution of numerical equations of the nth degree. Burnside and Panton's Theory of Equations. Fall term, full

study. Assistant Professor TOWNSEND. Required: Mat. 2, 4. 11. THEORY OF DETERMINANTS.—It is designed to give the student a thorough working knowledge of the subject and of its applications. It will, in general, cover the origin and notation