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Caption: Course Catalog - 1896-1897
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MATHEMATICS 167 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. Wood's Coordinate Geometry Winter term, full study. Professor SHATTUCK. Required: Math. 2, 4, 6, 7. 9. INTEGRAL CALCULUS.—Elementary forms of integration; in- tegrals 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. Byerly's 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. Rumside and Panton's Theory of Equations. Fall tei'm, full study. Associate Professor TOWNSEND, Required: Math. 2, 4. 11. THEORY OF DETERMINANTS.—The origin and notation of deter- minants, properties of determinants, determinant minors, multiplication of determinants, determinants of compound systems, determinants of special forms—Jacobians, Hessians, Wronskians—with applications to algebra, including linear transformations, and to analytic geometry. J/anus's Theory of Determinants, supplemented by lectures. Winter term, full study. Associate Professor TOWNSEND. Required: Math. 6, 7, 10. 12. THEOUY OF INVARIANTS.—The course will cover the general development of the theory of invariants, both from the geometric and from the algebraic side. Applications of invariants will be rnade to sys-
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