This book is compiled according to the Basic Requirements of Basic Mathematics Course Teaching for Engineering Undergraduates, which is formulated by the Teaching Guidance Sub-committee of Basic Mathematics Course for Non-mathematics Majors of the Ministry of Education. Contents include: function and limit, unary function calculus, vector algebra and spatial analytic geometry, multivariate function calculus, series, ordinary differential equations, etc. At the end of the book, there are three appendices including several commonly used plane curves and their equations, integral table and preliminary field theory, as well as reference answers for exercises. This book describes the basic concepts clearly and accurately, discusses the basic theories concisely and easily, selects typical examples and exercises, and emphasizes the cultivation of basic computing ability and the practical application of theories.