Vector Fields

Tutoring on Vector Fields

Learning Objectives:

Understand and Apply Vector Fields.

Math Tutoring on Vector Fields

A Vector is a quantity with magnitude and direction. Functions that assign a vector to a point on the plane or a point in space are called Vector Fields. They are useful for representing various types of Force Fields and Velocity Fields.

Definition of a Vector Field in Math Tutoring:

A Vector Field over a region R in a plane or 2D

where f and g are continuous over R’.

A Vector Field over a region V in space or 3D

where f, g and h are continuous over V’.

Graphing a 2D Vector Field by Hand:

To graph a Vector Field by hand, we need to plot several vectors in the Vector Field by selecting x and y values in the coordinate plane.

Sometimes it is helpful to plot several vectors with the same magnitude. Graphing Software is very helpful with plotting Vector Fields.





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Hook Questions:

1.    What is Vector Fields? Give the definition of it.

2.    How to graph a 2D Vector Field by hand?





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