Slope Field

Explore SlopeField on MathWorld

A slope field is a particular visualization of a linear, first-order differential equation in which the derivative at a given point is represented by a line segment of the corresponding slope.

Slope field is a college-level concept that would be first encountered in a differential equations course. It is an Advanced Placement Calculus AB topic.


Ordinary Differential Equation: An equality involving a function and its derivatives.
Vector Field: A vector field is a function that assigns a vector to each point of Euclidean space. Vector fields arise in differential equations and differential geometry.

Classroom Articles on Differential Equations (Up to College Level)

  • Bessel Function of the First Kind
  • Laplace Transform
  • Differential Equation
  • Partial Differential Equation
  • Euler Forward Method
  • Second-Order Ordinary Differential Equation
  • Fourier Transform
  • Separation of Variables