Function graphers, visualisation

Table of contents

1. Real functions
2. Implicit functions
3. Parametric curves
4. Discrete functions
5. Inequalities
6. Initial value problems

Real functions

• A function.
• Several functions.
• A function and its derivative.
• A function and its first three derivatives.
• Zeros of a function.
• Tangent of a function.
• An antiderivative.
• Integral representation of the gamma function..
• A family of functions.
• A distinction of cases.
• An interpolation polynomial.
• A family of interpolation polynomials.
• A table of some values of a function.
• Slider for one parameter.
• Slider for two parameters.
• Partial sum of a Fourier series.

Implicit functions

• An implicit function.
• An implicit function with asymptotes.
• A family of implicit functions.
• Gerono's lemniscate.

Parametric curves

• The unit circle.
• Gerono's lemniscate.
• A spiral.
• A clothoid.
• A family of parmetric curves.
• Metamorphosis.
• Applying a rotation matrix.
• Applying a family of rotation matrices.
• Tangential vector of a curve.
• TN-frame.
• Osculating circle.
• A smooth star.

Discrete functions

• A sequence in explicit form.
• A sequence in recursive form.
• A sequence with bounds.
• A series.
• Euler's totient function.
• A random walk.
• Hofstadter's Q sequence.
• Table of some values of a sequence.
• List of some values of a sequence.

Inequalities

• An inequality in one variable.
• An inequality in two variables.
• A system of inequalities. Covering visible.
• Solution set of the system.

Initial value problems

• A first order ODE. Initial values given by p:=[x0,y(x0)].
• A second order ODE. Initial values given by p:=[x0,y(x0),y'(x0)].
• For a function of time.
• A Picard iteration.
• Solving a system by matrix exponential.
• An autonomous system of two ODE.
• A non-autonomous system of two ODE.
• The one body problem. Stroboskopic view.
• The one body problem as a first order system.
• Scattering at a Coulomb potential.
• The Lorenz attractor. Projection on the xz plane.