Repository: UIHistories Project: Course Catalog - 1895-1896 [PAGE 181]

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MATHEMATICS

181

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. Byertys Integral Calculus. Spring term, full study. Professor SJIATTUCK. Required: Math. 2, 4, 6, 7, 8. 10. THEORY OP EQUATION'S.—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. Bunisidc and Pantori's Theory of Equations. Fall term, full study. Associate Professor

TOWNSENI).

Required: Math. 2, 4.

11. THEORY OF DETERMINANTS.—The origin and notation

of determinants, 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. Weld''s Theory of Determinants with selected chapters from Scott's Theory of Determinants. Winter term, full study. Associate Professor TOWNSEND. Required: Mathematics 2, 4, 6, 7. 12. THKORY 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 made to systems of conies and to Higher Plane Curves. Bruno's Biw'lren Pormen will be followed in part, but frequent use will • be made of Clebsch's Geo-