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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

    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 engineering. It provides engineers with the necessary tools to model, analyze, and solve complex problems in these domains, leading to advancements in technology and ...

  4. Malkus waterwheel - Wikipedia

    en.wikipedia.org/wiki/Malkus_waterwheel

    Its motion is governed by the Lorenz equations. While classical waterwheels rotate in one direction at a constant speed, the Malkus waterwheel exhibits chaotic motion where its rotation will speed up, slow down, stop, change directions, and oscillate back and forth between combinations of such behaviours in an unpredictable manner.

  5. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    [111] [115] This led to split mathematics into pure mathematics and applied mathematics, the latter being often considered as having a lower value among mathematical purists. However, the lines between the two are frequently blurred. [116] The aftermath of World War II led to a surge in the development of applied mathematics in the US and ...

  6. Real algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Real_algebraic_geometry

    Real algebra is the part of algebra which is relevant to real algebraic (and semialgebraic) geometry. It is mostly concerned with the study of ordered fields and ordered rings (in particular real closed fields ) and their applications to the study of positive polynomials and sums-of-squares of polynomials .

  7. Algebra - Wikipedia

    en.wikipedia.org/wiki/Algebra

    Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.

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