"New Engineering Mathematics Volume I" introduces the basics of selected topics in applicable mathematics i.e. matrices, three- dimensional analytical geometry, geometrical applications of differential calculus, functions of several variables and differential equations. Beginning with basic concepts, the topics are developed systematically with precision and elegance. Each chapter contains an introduction with the relevant definitions and concepts. The study of matrices and three-dimensional analytical geometry is complete in all respects. Geometrical applications of differential calculus include essentials on curvature, involutes, evolutes, and envelops. Partial differentiation of functions of several variables, its applications and ordinary differential equations are also discussed.