Geogebra Visualizations

Geogebra Apps for Algebra:

• Point Coordinate Practice

Geogebra Apps for Calculus:

• Area/Accumulation Functions

  • Accumulation Function Exploration Tool
    A tool to explore the accumulation function version of the Fundamental Theorem of Calculus.
  • Accumulation Function Curve Sketching Example 1
    Building an antiderivative accumulation function from a piece-wise derivative graph.

Geogebra Apps for Differential Equations:

• Bifurcation Motivation

  • Example 1, $\dfrac{dy}{dt} = y^2 + 2y + a$,  Dynamic graph of $f(y) = y’$ to illustrate Bifurcation

• Bifurcation Diagrams

  • Example 1, $\dfrac{dy}{dt} = y^2 + 2y + a$,  Bifurcation Diagram
    by Paul Seeburger
  • Bifurcation diagram for: $\dfrac{dy}{dt} =\frac{1}{50}(y^2 + ay + 16)$ 
    by Paul Seeburger
  • Saddle Node Bifurcation: y’ = y² + a
    Adapted from an app by Pablo Rodríguez Sánchez.
  • Pitchfork Bifurcation: y’ = y(a – y²)
    Adapted from an app by Pablo Rodríguez Sánchez.
  • Bifurcation diagram for: y’ = y³ – ay²
    New example adapted from an app by Pablo Rodríguez Sánchez.

• Second-order Slope Fields and Solution Curves

  • y” − 9y = 0
  • 2y” − 5y‘ − 3y = 0
  • y” + 4y’ + 3y = 0

• Second-order Repeated Root Solutions

  • Homogeneous case
  • Nonhomogeneous case: g(x) = x – 2
  • Nonhomogeneous case: g(x) = 2sin x
  • Nonhomogeneous case: g(x) = 2e^x

• Free and Forced Spring Motion

  • Spring Motion Demonstration (with/without Forcing)

• Laplace Transforms

  • Interactive Piecewise Function Plotter with the Unit Step Function

• Phase Portraits for Systems of Differential Equations

  • Example 1, Saddle Point
  • DE System Explorer, allows you to see the phase portrait of any 2 x 2 linear system of ODEs.