APEX Multivariable Calculus：本课程专为已有微积分基础，需要进一步学习多元微积分的同学设置。本课程是APEX Introduction to electromagnetism (APEX P05) 的前置课程。
本课程采用网络授课共12小时。希望同学们使用4-8小时左右时间完成课后作业。
Course Description: APEX M03: Multivariable Calculus
Reference book: Openstax: https://openstax.org/books/calculus-volume-3
*We do not require students to use the book for our course. Instead, we strongly recommend students to take notes and take advantage of lecture slides, lecture recordings, homework assignments, homework solutions, exams and office hours to enhance their learning outcome.
Contents:
Unit 1: Scalars and Vectors in 3D (2 hours)
Vector algebra and its applications in geometric problems of lines and planes.
Unit 2: Single Variable Vector Calculus (2 hours)
Cylindrical and spherical coordinates. Derivative and integration of vector valued single variable functions.
Unit 3: Partial Derivative and Gradient (2 hours)
Scalar and vector fields. Partial derivative, gradient, and directional derivative of scalar fields.
Unit 4: Integration in multiple dimensions (2 hours)
Integration of scalar fields in 2D and 3D spaces with surface and volume elements.
Unit 5: Derivatives and Integrations of Vector Fields (2 hours)
Divergence and curl of vector fields. Flux and line integral of vector fields. Gradient theorem.
Unit 6: Dimensional Reduction in Vector Field Integrations (2 hours)
Divergence theorem and Stokes theorem