especially how to ask new questions,think and analyze problems,gradually cultivate students'innovative thinking ability and mathematical modeling ability:by revealing the beauty in mathematics,combined with the teaching content,properly explain the scientist's dedication to science stories to strengthen quality education. 三、课程教学基本内容与要求 1.Chapter 10 Infinite sequences and series (1)master sequences,(2)master series, (3)master the integral test and estimates of sum, (4)master comparison tests,(5)master alternating series, (6)understand absolute convergence and the ratio and root test (7)master strategy of for testing series,(8)master power series, (9)understand representation of functions as power series, (10)Taylor and Maclaurin series,(11)The binomial series, (12)Applications of Taylor polynomials. 2.Chapter 11 Vectors and the Geometry of Space (1)master three-dimensional coordinate systems (2)master vectors,(3)master the dot product, (4)master the cross product, (5)master equations of lines and planes, (6)understand cylinders and quadric surfaces, (7)know cylindrical and spherical coordinates. 3.Chapter 12 Vector Functions (1)understand vector functions and space curves, (2)understand derivatives and integrals of vector functions, (3)understand arc length and curvature (4)know motion in space:velocity and acceleration. 4.Chapter 13 Partial Derivatives (1)master functions of several variables, (2)master limits and continuity, (3)master partial derivatives, (4)understand tangent planes and linear approximations, (5)master the chain rule, (6)understand directional derivatives and the gradient vector, (7)master maximum and minimum values.2 especially how to ask new questions, think and analyze problems, gradually cultivate students' innovative thinking ability and mathematical modeling ability; by revealing the beauty in mathematics, combined with the teaching content, properly explain the scientist's dedication to science stories to strengthen quality education. 三、 课程教学基本内容与要求 1. Chapter 10 Infinite sequences and series (1) master sequences, (2) master series, (3) master the integral test and estimates of sum, (4) master comparison tests, (5) master alternating series, (6) understand absolute convergence and the ratio and root test, (7) master strategy of for testing series,(8) master power series, (9) understand representation of functions as power series, (10) Taylor and Maclaurin series, (11) The binomial series, (12) Applications of Taylor polynomials. 2. Chapter 11 Vectors and the Geometry of Space (1) master three-dimensional coordinate systems, (2) master vectors, (3) master the dot product, (4) master the cross product, (5) master equations of lines and planes, (6) understand cylinders and quadric surfaces, (7) know cylindrical and spherical coordinates. 3. Chapter 12 Vector Functions (1) understand vector functions and space curves, (2) understand derivatives and integrals of vector functions, (3) understand arc length and curvature, (4) know motion in space: velocity and acceleration. 4. Chapter 13 Partial Derivatives (1) master functions of several variables, (2) master limits and continuity, (3) master partial derivatives, (4) understand tangent planes and linear approximations, (5) master the chain rule, (6) understand directional derivatives and the gradient vector, (7) master maximum and minimum values