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
To determine if a graph represents a linear function, a nonlinear function, or simply a relation, you should look at its shape. A linear function will produce a straight line, indicating a constant rate of change. If the graph curves or has varying slopes, it is a nonlinear function. If the graph does not represent a function at all (such as a vertical line), it is simply a relation.
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.
Nonlinear graphs represent relationships between variables that do not follow a straight line. Instead, the data points may form curves or other complex shapes, indicating that changes in one variable do not produce proportional changes in another. Common examples include quadratic, exponential, and logarithmic functions, which are used to model various phenomena in fields like physics, biology, and economics. Nonlinear graphs highlight the intricate dynamics and interactions within the data, making them essential for understanding complex systems.
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.