Here is a simple example of a nonlinear function.
Y = X2
=====Build on that!
y=x2 and y=lnx are two examples of nonlinear equations.
linear
A linear function would be represented by a straight line graph, so if it's not a straight line, it's nonlinear
Maybe possibly a piece-wise function...
No it is not.
The pitch of a note is a nonlinear function of its frequency. Specifically, pitch perception follows a logarithmic scale, meaning that equal frequency ratios correspond to equal perceived pitch intervals. For example, doubling the frequency of a note raises its pitch by an octave, which is a nonlinear relationship. Thus, while frequency itself is measured linearly, our perception of pitch is nonlinear.
The two-dimensional nonlinear Schrödinger equation is commonly referred to as the "Nonlinear Schrödinger Equation" (NLS). It describes the evolution of slowly varying wave packets in nonlinear media and is significant in various fields, including nonlinear optics and fluid dynamics. In its general form, it includes a nonlinear term that accounts for the interactions of the wave function with itself.
Nonlinear devices are components that do not follow a linear relationship between input and output. This means that their response is not proportional to the input signal. Examples include diodes, transistors, and nonlinear capacitors. Nonlinear devices are often used in electronic circuits to perform functions like signal processing and modulation.
Differentials can be used to approximate a nonlinear function as a linear function. They can be used as a "factory" to quickly find partial derivatives. They can be used to test if a function is smooth.
Any function in which the dependent variable is not exactly proportional to the zeroth or first power of the independent variable. E.g.: y(x) = a*(x+x^3); y(x) = a*exp(x); y(x) = a*sin(x); etc. This may be extended to differential equations by stating a nonlinear differential equation is one in which some function depends on a derivative which is not to the zeroth or first power. An example is: dy/dx - (y(x))^2 = a. Note, all of the values for "a" in these examples are meant to be constants.
A nonlinear Volterra integral equation is a type of integral equation where the unknown function appears under an integral sign and the relationship involves nonlinear terms. It typically has the form ( u(t) = f(t) + \int_{a}^{t} K(t, s, u(s)) , ds ), where ( K ) is a nonlinear kernel, ( f ) is a known function, and ( u(t) ) is the unknown function to be determined. These equations are often encountered in various fields such as physics, engineering, and biology, where they model systems with memory and time-dependent interactions. Solving nonlinear Volterra integral equations can be challenging, often requiring numerical methods or iterative approaches.
a roller coaster. It doesnt have a constaant rate of change