nonlinear

(noun)

A polynomial expression of degree 2 or higher.

Related Terms

  • conic section
  • inequality
  • system of equations
  • nonlinear function

(noun)

An algebraic term that is raised to the power of two or higher; equivalently, a function with a curved graph.

Related Terms

  • conic section
  • inequality
  • system of equations
  • nonlinear function

Examples of nonlinear in the following topics:

  • Nonlinear Systems of Inequalities

    • Systems of nonlinear inequalities can be solved by graphing boundary lines.
    • A nonlinear inequality is an inequality that involves a nonlinear expression—a polynomial function of degree 2 or higher.
    • All points below the line $y=x+2$ satisfy the linear equality, and all points above the parabola $y=x^2$ satisfy the parabolic nonlinear inequality.
    • This need not be the case with all nonlinear inequalities, but reversing the direction of both inequalities in the previous example would lead to an infinite solution area.
    • This graph of a cubic function is an example of a nonlinear equation.
  • Models Involving Nonlinear Systems of Equations

    • Nonlinear systems of equations can be used to solve complex problems involving multiple known relationships.
    • The conservation of mechanical energy can produce a system of nonlinear equations when there is an elastic (perfectly bouncy) collision.
    • Rendering and visualizing these objects, and formulating a plan for constructing them, requires the software to solve nonlinear systems.
    • In addition to practical scenarios like the above, nonlinear systems can be used in abstract problems.
    • Extend the ideas behind nonlinear systems of equations to real world applications
  • Nonlinear Systems of Equations and Problem-Solving

    • As with linear systems, a nonlinear system of equations (and conics) can be solved graphically and algebraically for all of its variables.
    • Nonlinear systems of equations, such as conic sections, include at least one equation that is nonlinear.
    • A nonlinear equation is defined as an equation possessing at least one term that is raised to a power of 2 or more.
    • Since at least one function has curvature, it is possible for nonlinear systems of equations to contain multiple solutions.
    • Solving nonlinear systems of equations algebraically is similar to doing the same for linear systems of equations.
  • Linear and Quadratic Equations

    • Since terms of linear equations cannot contain products of distinct or equal variables, nor any power (other than 1) or other function of a variable, equations involving terms such as $xy$, $x^2$, $y^{\frac{1}{3}}$, and $\sin{x}$ are nonlinear.
Subjects
  • Accounting
  • Algebra
  • Art History
  • Biology
  • Business
  • Calculus
  • Chemistry
  • Communications
  • Economics
  • Finance
  • Management
  • Marketing
  • Microbiology
  • Physics
  • Physiology
  • Political Science
  • Psychology
  • Sociology
  • Statistics
  • U.S. History
  • World History
  • Writing

Except where noted, content and user contributions on this site are licensed under CC BY-SA 4.0 with attribution required.