Most vector fields encountered in engineering and natural sciences are force fields. In mathematics, these and other fields are grouped under the term gradient fields. The calculation of vector curve integrals in such fields generally becomes much simpler: One determines a primitive function of the field and obtains the value of the vector curve integral by substituting the start and end point of the curve into the primitive function; the difference between these values is the value of the vector curve integral. In particular, the value is not dependent on the course of the curve.

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Gradient Fields

  • Christian Karpfinger

摘要

Most vector fields encountered in engineering and natural sciences are force fields. In mathematics, these and other fields are grouped under the term gradient fields. The calculation of vector curve integrals in such fields generally becomes much simpler: One determines a primitive function of the field and obtains the value of the vector curve integral by substituting the start and end point of the curve into the primitive function; the difference between these values is the value of the vector curve integral. In particular, the value is not dependent on the course of the curve.