The present work is a revision and abridgment of the authors’ Course in Mathematics for Students of Engineering and Applied Science . The condensation of a two-volume work into a single volume has been made possible partly by the omission of some topics, but more especially by a rearrangement of subject matter and new methods of treatment. Among the subject omitted are determinations, much of the general theory of equations, the general equation of the conic sections, polars and diameters related to conics, center of curvature, evolutes, certain special methods, of integration, complex numbers, and some types of differential, can well be postponed to a latter course, of subjects which are more immediately important.