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  2. Applied mathematics - Wikipedia

    en.wikipedia.org/wiki/Applied_mathematics

    A numerical solution to the heat equation on a pump casing model using the finite element method.. Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational methods, and numerical analysis); and applied probability.

  3. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    The application of linear algebra in this context is vital for the design and operation of modern power systems, including renewable energy sources and smart grids. Overall, the application of linear algebra in fluid mechanics, fluid dynamics, and thermal energy systems is an example of the profound interconnection between mathematics and ...

  4. Mathematical model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_model

    The floating model rests on neither theory nor observation, but is merely the invocation of expected structure. Application of mathematics in social sciences outside of economics has been criticized for unfounded models. [5] Application of catastrophe theory in science has been characterized as a floating model. [6] Strategic vs. non-strategic.

  5. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Algebra is the art of manipulating equations and ... were shown to have applications outside mathematics; ... predictions that can be tested against real-world data. ...

  6. Algebra - Wikipedia

    en.wikipedia.org/wiki/Algebra

    Solving an equation corresponds to adding and removing objects on both sides in such a way that the sides stay in balance until the only object remaining on one side is the object of unknown mass. [145] Word problems are another tool to show how algebra is applied to real-life situations. For example, students may be presented with a situation ...

  7. Numerical analysis - Wikipedia

    en.wikipedia.org/wiki/Numerical_analysis

    The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.

  8. Differential equation - Wikipedia

    en.wikipedia.org/wiki/Differential_equation

    In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. [1] In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.

  9. Lorenz system - Wikipedia

    en.wikipedia.org/wiki/Lorenz_system

    A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = ⁠ 8 / 3 ⁠. The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz.

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