This book is a textbook for the 12th Five-Year Plan, the 11th Five-Year Plan and the 2 1 century-oriented undergraduate planning of general higher education. The contents include several series, function series and function series, power series, Fourier series, limit and continuity of multivariate function, differential calculus of multivariate function, implicit function theorem and its application, parametric integral, curve integral, multiple integral, surface integral, vector function differential calculus and so on. This revision has made some adjustments on the basis of the fourth edition, making the teaching materials more logical and supplementing the digital resources appropriately. The fifth edition still maintains the characteristics of the first four editions, such as "appropriate content selection, simple explanation, easy teaching and learning, and strong readability". This book can be used as a textbook for mathematics and other related majors in colleges and universities (fifth edition) (second volume).