nonlinear

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.