Topics include the technique of differentiation; maxima and minima, rates, curvature, parametric equations, differentials, series, and partial differentiation; technique of integration; areas, volumes, lengths, surfaces, centroids, moments of inertia, fluid pressure, work, multiple integrals, and approximate integration by Simpson’s Rule.

The theory and technique of both differentiation and integration are studied during the first term, with a few simple applications, mostly geometric in character. The second term affords opportunity for many practical applications from various fields of engineering. The aim of a set of general review problems during the last few weeks is to teach not only how to use the methods previously studied, but when to use them—i.e., whether the nature of a problem suggests an exact analytical solution, or an approximate or graphical solution.

Texts: Granville-Smith-Longley, “Elements of the Differential and Integral Calculus”; N. C. E. “Laboratory Manual for a Course in Calculus”.

Math 31, 32.

Two advanced courses, Differential Equations (first term) and Vector Analysis (second term), are optional for Juniors in addition to the work of the regular curriculum. No attempt will be made to give an exhaustive mathematical treatment, but certain parts of these subjects will be taught together with other related material necessary for the solution of important problems in all branches of engineering.

Text: Doherty and Keller, “Mathematics of Modern Engineering”. Vol I.

Math 31 Differential Equations. First and second order equations of common occurrence; linear differential equations of any order with constant coefficients, and systems of linear equations; determinants; Fourier series and harmonic analysis.

Math 32 Vector Analysis. Algebra and calculus of vectors; line and surface integrals, and potential theory; vector operators, and their application to electromagnetic theory and the derivation of certain partial differential equations of mathematical physics.

DEPARTMENT OF MECHANICS