This book is an advanced mathematics textbook for ordinary undergraduate colleges. For the students who take advanced mathematics courses for one year in the "Excellent Engineer Education and Training Plan". The determination and expression of the content of the textbook fully considers the actual situation of students' ability level and learning motivation. While imparting mathematical knowledge, we should properly integrate the background knowledge and application cases of related majors of "Excellent Engineer Training Program". This book is divided into two volumes, the first volume includes function, limit and continuity, differential calculus of unary function, integral calculus of unary function and differential equation; The second volume includes spatial analytic geometry and vector algebra, differential calculus of multivariate functions, integral calculus of multivariate functions and infinite series. This book can be used as a textbook for advanced mathematics courses for science and engineering majors in ordinary undergraduate colleges. This textbook is readable and can also be used as a reference book for other readers.