This book is compiled with reference to the Basic Requirements for the Teaching of Basic Mathematics Courses for Engineering Undergraduates formulated by the Steering Committee for Mathematics and Statistics Teaching in Colleges and Universities of the Ministry of Education. This book is divided into two volumes. The first volume includes function, limit and continuity, derivative and differential, mean value theorem and application of derivative, indefinite integral, definite integral, application of definite integral, ordinary differential equation, etc. At the end of the book, there are basic elementary functions and hyperbolic functions, a brief introduction to polar coordinates, several common curves, integral tables and reference answers to exercises. This book is equipped with appropriate exercises. The total exercises in each chapter are divided into two groups: A and B. Group A focuses on basic concepts and methods, which students must master. Group B questions are difficult, comprehensive and argumentative, so as to meet the increasing demand of graduate students.