(8)understand Langrange multipliers 5.Chapter 14 Multiple Integrals (1)master double integral over rectangle, (2)master iterated integrals, (3)understand double integral over general regions, (4)understand double integrals in polar coordinates (5)master applications of double integrals (6)understand surface area,(7)understand triple integrals, (8)know triple integrals in cylindrical and spherical coordinates, (9)know change of variables in multiple integrals. 6.Chapter 15 Vector Calculus (know) (1)vector fields.(2)line integrals. (3)the fundamental theorem for line integrals, (4)Green's theorem,(5)curl and divergence, (6)parametric surfaces and their areas,(7)surface integrals, (8)Stokes'theorem,(9)the Divergence theorem,(10)summary. 7.Chapter 16 First-Order Differential Equations (1)master first-order differential equations. 8.Chapter 17 Second-Order Differential Equations (1)master second-order linear equations, (2)master nonhomogeneous linear equations. 四、 课程学时分配 课内 课外 教学内容 讲授 测验 学时 学时 小计 1.Infinite sequences and series 10 10 2.Vectors and the Geometry of Space R 3.Vector Functions 8 4.Partial Derivatives 5.Multiple Integrals 6.Vector Calculus 7.First-Order Differential Equations6 8.Second-Order Differential Equations 9.Revision 合 计 64 64 3 (8) understand Langrange multipliers. 5. Chapter 14 Multiple Integrals (1) master double integral over rectangle, (2) master iterated integrals, (3) understand double integral over general regions, (4) understand double integrals in polar coordinates, (5) master applications of double integrals, (6) understand surface area, (7) understand triple integrals, (8) know triple integrals in cylindrical and spherical coordinates, (9) know change of variables in multiple integrals. 6. Chapter 15 Vector Calculus (know) (1) vector fields, (2) line integrals, (3) the fundamental theorem for line integrals, (4) Green’s theorem, (5) curl and divergence, (6) parametric surfaces and their areas, (7) surface integrals, (8) Stokes’ theorem, (9) the Divergence theorem, (10) summary. 7. Chapter 16 First-Order Differential Equations (1) master first-order differential equations. 8. Chapter 17 Second-Order Differential Equations (1) master second-order linear equations, (2) master nonhomogeneous linear equations. 四、 课程学时分配 教学内容 讲授 测验 课内 学时 小计 课外 学时 1. Infinite sequences and series 10 10 2. Vectors and the Geometry of Space 8 8 3. Vector Functions 8 8 4. Partial Derivatives 8 8 5. Multiple Integrals 8 8 6. Vector Calculus 8 8 7. First-Order Differential Equations 6 6 8. Second-Order Differential Equations 4 4 9.Revision 4 4 合 计 64 64