vector fields
(50 minutes to learn)
Summary
A vector field is a function associating a vector with each point. Common examples include flow fields, force fields, and gradients of functions.
Context
This concept has the prerequisites:
Goals
- Understand what a vector field is
- Know some common examples (gradients of functions, force fields, velocity fields)
- Be able to visualize vector fields graphically
Core resources (read/watch one of the following)
-Free-
→ MIT Open Courseware: Multivariable Caclulus (2010)
Video lectures for MIT's introductory multivariable calculus class.
-Paid-
→ Multivariable Calculus
An introductory multivariable calculus textbook.
Location:
Section 15.1, "Vector fields," pages 1014-1018
Additional dependencies:
- partial derivatives
See also
- The gradient of a function is a common example of a vector field.
- Some operations which can be applied to vector fields: