Examples for

Applied Mathematics

Applied mathematics is the branch of mathematics devoted to utilizing and applying the results, techniques and methods of mathematics and specific subject-area expertise to understand and solve real-world problems in science, technology, business, society, engineering and industry. Wolfram|Alpha's broad base of computational knowledge and powerful mathematical algorithms allows you to apply mathematical techniques to compute, analyze and explore a variety of problems encountered in practical applications.


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:

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Dynamical Systems

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:

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Game Theory

Get information about and analysis of the risks and rewards of cooperation and conflict in a variety of mathematical games.

Get information about a mathematical game:

Numerical Analysis

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:

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Ask about fractals both over real and complex domains.

Plot fractals given by dynamical systems:

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  • Calculus & Analysis
  • Computational Sciences
  • Differential Equations
  • Physics
  • Packing & Covering of Objects

    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:

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