The term isocline derives from the Greek words for "same slope." For a first-order ordinary differential equation y^'=f(t,y) is, a curve with equation f(t,y)=C for some constant C is known as an isocline. In other words, all the solutions of the ordinary differential equation intersecting that curve have the same slope C. Isoclines can be used as a graphical method of solving an ordinary differential equation.

The term is also used to refer to points on maps of the world having identical magnetic inclinations.

See also

Isoclinal Line, Isoclinal Plane, Slope Field

Explore with Wolfram|Alpha


Hollis, S. Differential Equations with Boundary Value Problems. Upper Saddle River, NJ: Prentice Hall, p. 53, 2002.Kármán, T. von and Biot, M. A. Mathematical Methods in Engineering: An Introduction to the Mathematical Treatment of Engineering Problems. New York: McGraw-Hill, pp. 3 and 7, 1940.

Referenced on Wolfram|Alpha


Cite this as:

Weisstein, Eric W. "Isocline." From MathWorld--A Wolfram Web Resource.

Subject classifications