Repository: UIHistories Project: Course Catalog - 1873-1874 [PAGE 49]

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Departments.

ALGEBRA.

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surfaces, and the measurement of their lengths, areas and volumes. Powers, roots and radicals of any degree; Binomial Theorem, Properties and summation of series, Exponential quantities, Logarithms, General theory and methods of solving equations. ADVANCED GEOMETRY. Application of Algebra to Geometry, Transversals, Harmonic Proportion, etc. TRIGONOMETRY. Analytical, Plane and Spherical. Relations between the functions of an arc, Formation and use of tables, Solution of plane and spherical triangles. 2. ANALYTICAL GEOMETRY. Construction of equations by means of co-ordinates; Discussion in a plane of the point, right-line, circle, ellipse, parabola and hyperbola; Higher plane curves, cycloid, cissoid of Diodes, etc. DIFFERENTIAL CALCULUS. Differentials of algebraic and transcendental functions, Maclaurin's Theorem, Taylor's Theorem, Maxima and minima of functions, Equation of Tangents, normals, subtangents, sub-normals, etc.; Differentials of lines, surfaces and volumes. INTEGRAL CALCULUS. Integration of known forms and of rational fractions, Rectification of curves, quadrature of plane areas and surfaces of revolution, and cubature of solids of revolution. 3. ANALYTICAL GEOMETRY. Loci in space ; Surfaces of the second order. DIFFERENTIAL CALCULUS. Differentials and maxima and minima of functions of two or more variables, Osculatory curves, radius of curvature; Evolutes, involutes, envelopes; Discussion of algebraic and transcendental curves and surfaces; Tangent plane and normal, Partial differentials of surfaces and volumes. INTEGRAL CALCULUS. Integration of transcendental and irrational differentials, Differentials of higher orders, Differential equations, Rectification, quadrature and cubature in general; Calculus of Variations.

PHYSICS.

A Physical Laboratory has been established in the New Building, and amply furnished, by special state appropriation, with apparatus for experimental investigation. Here the student, in connection with the study of the principles, carefully repeats many of the most important experiments. Special attention is given to molecular force, properties of matter, laws of undulation, spectrum analysis, laws of heat, electricity and magnetism. Chemical Physics is given in a special course of lectures.

ASTRONOMY AND GEODESY.

Temporary arrangements have been made for Observatory Practice by the erection of a small observatory and the mounting of instruments of convenient size for students' use. DESCRIPTIVE ASTRONOMY is given by lectures, with Lockyer's Astronomy for a text-book. The Equatorial Telescope is in constant use during favorable weather. PRACTICAL ASTRONOMY is given by lectures, practical work with the Meridian Circle, Sextant, Theodolite, etc., and Astronomical Calculations. GEODESY is given by lectures, practice and calculations. Some first-class instruments have been ordered and trigonometrical stations will be erected.