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所在平台: Udemy |
课程主页: https://www.udemy.com/course/calculus-2-ch-111-134-to-138-142-to-145-148/
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Coursera 课程《多元微积分 II》涵盖了多变量微积分中的一系列核心主题，并提供了相应的练习题以巩固理解。 课程内容包括： * **三维空间中的直角坐标系** (11.1节)：涵盖练习题 1, 13a, 19-22, 23, 35。 * **微分** (13.4节)：通过练习题 9, 15 探索变量变化对函数的影响。 * **链式法则** (13.5节)：练习题 1, 7 侧重于复合函数的求导。 * **方向导数与梯度** (13.6节)：练习题 5, 17, 45 旨在加深对多方向变化率的理解。 * **切平面与法向量** (13.7节)：选取练习题 1, 12 进行练习。 * **二元函数的最大值与最小值** (13.8节)：通过练习题 11, 16 学习优化问题。 * **非直角区域上的二重积分** (14.2节)：包含练习题 1, 15, 21, 30, 39。 * **极坐标下的二重积分** (14.3节)：练习题 5, 7, 27 提供实践。 * **曲面面积** (14.4节)：练习题 5, 8。 * **三重积分** (14.5节)：包含练习题 9, 10。 * **柱坐标和球坐标下的三重积分** (14.8节)：练习题 4, 11, 15。 本课程旨在帮助学习者建立对三维几何、偏导数以及多重积分的扎实掌握。
Sec 11.1 (pg. 777): Rectangular Coordinates in 3-Space - Exercises: 1, 13a, 19-22, 23, 35Sec 13.4 (pg. 947): Differentials - Exercises: 9, 15Sec 13.5 (pg. 956): The Chain Rule - Exercises: 1, 7Sec 13.6 (pg. 966): Directional Derivatives and Gradients - Exercises: 5, 17, 45Sec 13.7 (pg. 975): Tangent Planes and Normal Vectors - Exercises: 1, 12Sec 13.8 (pg. 985): Maxima and Minima of Functions of Two Variables - Exercises: 11, 16Sec 14.2 (pg. 1051): Double Integrals over Nonrectangular Regions - Exercises: 1, 15, 21, 30, 39Sec 14.3 (pg. 1024): Double Integrals in Polar Coordinates - Exercises: 5, 7, 27Sec 14.4 (pg. 1034): Surface Area - Exercises: 5, 8Sec 14.5 (pg. 1054): Triple Integrals - Exercises: 9, 10Sec 14.8 (pg. 1077): Triple Integrals in Cylindrical and Spherical Coordinates - Exercises: 4, 11, 15In this course, we will cover a wide range of important topics in multivariable calculus. The assigned exercises are designed to build a strong understanding of three-dimensional geometry, partial derivatives, and multiple integrals. From Section 11.1 (pg. 777) on Rectangular Coordinates in 3-Space, the selected exercises are 1, 13a, 19-22, 23, 35. Moving to differentials in Section 13.4 (pg. 947), exercises 9 and 15 will help us explore how small changes in variables affect functions.In Section 13.5 (pg. 956) on the Chain Rule, exercises 1 and 7 provide practice on differentiating composite functions. For Directional Derivatives and Gradients in Section 13.6 (pg. 966), exercises 5, 17, and 45 are assigned to deepen understanding of rates of change in multiple directions. In Section 13.7 (pg. 975) on Tangent Planes and Normal Vectors, exercises 1 and 12 are selected.We will then study optimization in Section 13.8 (pg. 985) by solving exercises 11 and 16 on finding maxima and minima of functions of two variables. In Section 14.2 (pg. 1051) on Double Integrals over Nonrectangular Regions, exercises 1, 15, 21, 30, and 39 are given. Further practice with Double Integrals in Polar Coordinates in Section 14.3 (pg. 1024) includes exercises 5, 7, and 27. For Surface Area in Section 14.4 (pg. 1034), exercises 5 and 8 are listed. Finally, for Triple Integrals in Section 14.5 (pg. 1054), exercises 9 and 10 are assigned, and Triple Integrals in Cylindrical and Spherical Coordinates from Section 14.8 (pg. 1077) cover exercises 4, 11, and 15.
