Find a stream function for a given two-dimensional vector field by integrating its partial derivatives.

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Finding a Stream Function for a Divergence-Free Vector Field

Multivariable calculus core

Find a stream function for vector field \(\mathbf{F}(x, y) = \langle x \sin y, \cos y \rangle\).

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What you need first

definition of a stream function
divergence of a vector field
partial derivatives
integration with respect to one variable

What this problem tests

Tests the ability to verify if a vector field is divergence-free and to recover a scalar function from its partial derivatives.

This problem typically appears in a multivariable calculus or fluid dynamics course when discussing vector fields, divergence, and incompressible flow.

Finding a Stream Function for a Divergence-Free Vector Field

What you need first

What this problem tests

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