Course Description: This course is designed for students who already have a foundation in calculus and need to further study multivariable calculus. It serves as a prerequisite for APEX Introduction to Electromagnetism (APEX P05).
The course is delivered online and consists of a total of 12 hours of instruction. Students are expected to spend approximately 4–8 hours completing homework assignments.
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