Calculus

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Fields surrounding u and v.

This illustration shows three vector field diagrams related to two functions u and v, each depicting the directional flow of these scalar fields across the xy-plane. Each panel captures different behavior and patterns of the functions with respect to the axes and the directional fields. The vector arrows indicate the flow and magnitude of the fields in the positive and negative directions.

Three vector field diagrams showing flow around functions u and v in Cartesian coordinates. The first panel illustrates radial convergence at the origin, the second features linear flow along the diagonal y = x, and the third displays a complex saddle point flow. The vector arrows indicate the flow and magnitude of the fields in the positive and negative directions.

This illustration is ideal for mathematics, physics, and engineering textbooks to teach vector calculus, field theory, and dynamic systems.

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