Repository: UIHistories Project: Course Catalog - 1899-1900 [PAGE 233]

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MATHEMATICS

231

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. Byerl/s Integral Calculus. II.; daily; section A, 1; section B, 2; section C, 4; (5).

Professor SHATTUCK and Mr. SHORT.

Required:

10.

Mathematics 7.

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. I.; M., W., F.; 1; (3). Associate Professor

TOWNSEND and Mr. COAR.

Required:

11.

Mathematics 2, 4 or 1, 3.

THEORY OF DETERMINANTS.—The origin and notation of de-

terminants, properties of determinants, determinant minors, multipication of determinants, determinants of compound systems, determinants of special forms—Jacobians, Hessians, Wronskians—with applications to algebra, including linear transformations, and to analytic geometry. Hanus's Theory of Determinants, supplemented by lectures. / . ; Tu., Th.; 1; (2). Associate Professor TOWNSEND and

Mr. COAR.

Required: Mathematics 7, 10. 12. THEORY 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. Lectures with collateral reading. Associate Professor TOWNSEND. Required: Mathematics 11.

13. THEORY OF FUNCTIONS.—By way of introduction, consider-

able attention will be given to the geometric representation of the complex variable, including Argand's diagram, conformal representation, and harmonic ratios, and bilinear transformation. This will be followed by the development of the theory of infinite series, algebraic and transcendental functions, integration of uniform functions, Riemann's surfaces, introduction to elliptic functions, etc. Durege's Theory of Functions and Collateral Reading. I. and II.; M., W., F.;

31 (3)Associate Professor TOWNSEND and Mr. COAR.

Required:

Mathematics 7, 9, 10.