Applied Mathematics

Find global and local extrema and stationary points of functions or impose a constraint on a function and compute the constrained extrema.

Minimize or maximize a function:

Minimize or maximize a function of several variables:

Minimize or maximize a function subject to a constraint:

Use numerical analysis to compute roots of equations, to solve numerical integrals and to solve ordinary differential equations.

Find a root of an equation using Newton's method:

Use numerical methods to find roots of numbers:

Approximate an integral using a specified numerical method:

Solve an ODE using a numerical method:

Use Wolfram|Alpha to explore discrete- and continuous-time dynamical systems and control systems.

Analyze the logistic map:

Analyze the Lotka–Volterra predator‐prey model:

Ask about fractals both over real and complex domains.

Plot fractals given by dynamical systems:

Estimate the number of objects required to pack or cover another object.

Estimate the number of objects required to fill a container:

Estimate the number of objects required to cover a specified area:

Estimate the number of objects required to circle another object: