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Caption: Course Catalog - 1898-1899
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218 GENERAL DESCRIPTION OF COURSES curves. The course will also include a discussion of the following subjects: Coordinate systems for a point in space, the locus in space of an equation of the first and second degree, planes and straight lines, quadratic surfaces. Tanner and Allen's Analytic Geometry. II.; daily; section A, i; section B, 3; section C, 6; (5). Mr. BRENKE, Mr MILNE and Mr. COAR. Required: Mathematics 2, 4 or 1, 3. 7. DIFFERENTIAL CALCULUS.—Variables and functions; limits and infinitesimals; differentials and derivatives; differentiation of explicit functions, implicit functions, and functions of several variables ; derivatives of higher orders; successive derivatives, developments in series; maxima and minima of functions; indeterminate forms; plane curves, tangents, and normals; asymptotes, singular points, and curve tracing; theory of envelopes, of curvature, of evolutes, and of involutes. Byerly's Differential Calculus. I.; daily; section A, 1; section B, 2; (5). Professor SHATTUCK. Required: Mathematics 6. 9. INTEGRAL CALCULUS.—Elementary forms of integrations; 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. Byerly's Integral Calculus. II.; daily; section A, 1; section B, 2; (5). Professor SHATTUCK. Required: Mathematics 7. 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. I.; M., W.,F.; 1; (3). Mr. COAR. Required: Mathematics 2, 4 or 1, 3.
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