DEPARTMENT OF MATHEMATICS

Confidence in his ability to solve the mathematical problems which will confront him in training and practice is a very necessary qualification for the successful student of engineering. Not only must he be able to solve these problems, but he must know that his solutions are correct. The courses in mathematics given to all students during the freshman and sophomore years aim to provide this confidence.

Emphasis is placed not on acquiring information, but on developing skill,—skill in analyzing problems and arriving accurately and efficiently at their solution. Consequently, much time is given to written work under careful supervision of the instructors. Neatness and orderly arrangement are stressed, as well as efficiency of methods and the checking of results.

In the sophomore year the same division of time between classroom recitations and written exercises is continued. Here the student adds a powerful tool to his equipment in the theory of the differential and integral calculus. Applications of the methods studied include many practical problems from various types of engineering work.

Beside the minimum requirements for completing the courses mentioned above, a large number of extra problems is included to provide further training for students of superior ability. For those who plan to go into fields of research or to continue their studies after graduation, the Department offers certain advanced courses designed as preparation for graduate work. These may be elected by upper classmen in addition to the regular courses.

SUBJECTS OF INSTRUCTION
in the
DEPARTMENT OF MATHEMATICS

Math 1 Freshman Mathematics.

In order to enable him to handle accurately and efficiently the mathematics of engineering subjects, the student is given a thorough training in the analysis and solution of problems, and in the performance of numerical calculations, including the use of slide-rule and logarithmic methods.

The following subject matter will be included:

Plane Trigonometry: review of the solution of right and oblique triangles and fundamental trigonometric analysis.

Geometry: review of the use of mensuration formulas for plane and solid figures.

Algebra: review of fundamental operations, and simplification of fractional forms; solution of equations and simultaneous equations, linear and quadratic, and the approximate solution of equations of higher degree; exponents and radicals; complex numbers, variation, binominal theorem, and progressions (with applications to compound interest and annuities).

Analytic Geometry: fundamental formulas; general curve plotting; equations of the straight line, circle and conic sections (with applications); polar coordinates; translation and rotation of axes; and an introduction to solid analytic geometry.

Texts: Oglesby and Cooley, “Plane Trigonometry”; Pettit and Luteyn, “College Algebra”; H. B. Phillips, “Analytic Geometry”.

Math 21 Calculus. Prerequisite, Math 1.

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.