Isocline

The term isocline (from the Greek isos = equal and klínein = tend ) means in mathematics and geophysics a curve of equal inclination.

Isoclines in mathematics

In mathematics isoclines are a tool for graphical integration, ie to the drawings determination of approximate solutions of a differential equation.

For an explicit differential equation each curve is an equation of the type ( at constant ) an isocline. In the intersection points of different dissolution profiles of the differential equation with the solution of the isocline curves have the same pitch ( ie ) and therefore the same inclination angle relative to the axis.

Example

For the differential equation is a Isoklinengleichung respectively. The isoclines in this example, that is, the straight line passing through the origin with the exception of the -axis. The solutions of the differential equation have ( at least locally ) the form. The corresponding solution curves are parabolas; obtained for the axis as another solution curve.

The two sketches show some of the isoclines (red). From the short line segments ( line elements ) in each case the corresponding slope can be read. In the right sketch some solution curves (blue) are also shown.

Isoclines in Geophysics

In geophysics the term isocline is used for lines of equal magnetic inclination. Such isocline connects points with each other, in which include the field lines of the geomagnetic field at the same angle relative to the earth's surface.

Zero Kline

A special case is the zero Kline, applies.