Repository: UIHistories Project: Board of Trustees Minutes - 1871 [PAGE 43]

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functions of two or more variables; tendency of curves to coincide; osculatory curves; radius of curvature; evolutes and involutes; envelopes; construction and discussion of algebraic curves, the logarithmic curve, the cycloid, spirals; general surfaces; equations of tangent plane and normal line; partial differentials of a surface and of a volume. Integral Calculus; integration of the differentials of circular functions and of circular arcs; of certain irrational differentials; of differentials containing transcendental quantities; of the differentials of the higher orders; and of differential equations; rectification and quadrature of curves ; eubature of volumes in general. Second Term.—Calculus of Variations. Method of Least Squares. H I S T O R Y A N D SOCIAL S C I E N C E .

The instruction in this Department will be given partly with text books, but chiefly by lectures, with systematic readings of specified authors, and daily examinations on the same. The study of historical geography will keep even pace with the history studied, and the chronology will be rendered as clear and distinct as possible. Written exercises on chronology, and essays in historical criticism, will constitute prominent features of the course.

FIRST YEAR—First Term.—Discovery, settlement and colonial history of the United States, with notices of other American States; American geography. Two lectures (or lessons) a week. Second Term.—History of the United States from the time of the Revolution. Two lectures (or lessons) a week. SECOND YEAR—First Term.—Ancient History of Greece and Rome, with notices of other ancient nations; ancient Geography. Five lessons (or lectures) a week. Second Term.—Mediaeval history. Third Term. Modern history—general European history: European geography. Five lessons (or lectures) a week. Political economy. THIRD YEAR—First Term.—Constitutional history of England, and of the United States. Two lectures a week. Second Term.—History of Civilization; analysis of historical forces and phenomena; notices of the history of the arts and of the inductive sciences. Third Term. — Political philosophy; constitutional and international law. COMMERCIAL.

The course in this Department will occupy one year, the first term of which will be occupied in teaching the principles of book-keeping in general; the second, their application to special lines of business, general business forms and papers, and the third, to the higher operations of a counting house, commercial law and political economy. Students who wish to prepare for a commercial career, and also acquire a general education, may extend this course through two or more years, by taking such collateral studies as their contemplated vocation may render desirable. Studies recommended for this purpose, would be: The English and German Languages, Mathematics, one or'two terms of Chemistry (for druggists, etc.), and History.

First Term.—Book-keeping by single and double entry; theory of mercantile accounts, arid the several principal and auxiliary books. Penmanship; commercial calculations.