In mathematics, a **slope field** (or **direction field**) is a graphical representation of the solutions of a first-order differential equation. It is achieved without solving the differential equation analytically, and thus it is useful. The representation may be used to qualitatively visualize solutions, or to numerically approximate them.

Read more about Slope Field: General Application, Examples

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**Slope Field**- Examples

... y' = xy

**Slope field**Integral curves Isoclines (blue),

**slope field**(black), and some solution curves (red) ...

Autonomous System (mathematics) - Example

... To plot the

... To plot the

**slope field**and isocline for this equation, one can use the following code in GNU Octave/MATLAB Ffun = @(X,Y)(2-Y).*Y % function f(x,y)=(2-y)y =meshgrid(0.2 ... ezplot(y3, ) ezplot(y4, ) ezplot(y5, ) ezplot(y6, ) title('**Slope field**, isoclines and solutions for f(x,y)=(2-y)y') ...### Famous quotes containing the word field:

“It is through attentive love, the ability to ask “What are you going through?” and the ability to hear the answer that the reality of the child is both created and respected.”

—Mary *Field* Belenky (20th century)

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