Concepts: Linear and Nonlinear | NECSI
Linear and non-linear relationships demonstrate the relationships between two quantities. The graph of a linear equation forms a straight line. What Is the Difference between Linear and Nonlinear Equations in term to fit the curved relationship between BMI and body fat percentage. Non-linear relationship is fundamental to most physical and statistical phenomena and their study is important to fully understand the world around.
Linear & nonlinear functions: table (video) | Khan Academy
Nonlinear relationships, in general, are any relationship which is not linear. What is important in considering nonlinear relationships is that a wider range of possible dependencies is allowed.
When there is very little information to determine what the relationship is, assuming a linear relationship is simplest and thus, by Occam's razor, is a reasonable starting point. However, additional information generally reveals the need to use a nonlinear relationship.
Many of the possible nonlinear relationships are still monotonic. This means that they always increase or decrease but not both.
Monotonic changes may be smooth or they may be abrupt. For example, a drug may be ineffective up until a certain threshold and then become effective.
Linear & nonlinear functions: table
However, nonlinear relationships can also be non-monotonic. For example, a drug may become progressively more helpful over a certain range, but then may become harmful.
Thus the degree of help increases and decreases and this is a non-monotonic, as well as a nonlinear, relationship. These are commonly occurring relationships between variables. For example, the pressure and volume of nitrogen during an isentropic expansion are related as PV1.
Next, a number of non-linear relationships are monotonic in nature. This means they do not oscillate and steadily increase or decrease.
Linear and non-linear relationships | Student assessment
This is good to study because they behave qualitatively like linear relationships for a number of cases. Approximations A linear relationship is the simplest to understand and therefore can serve as the first approximation of a non-linear relationship. The limits of validity need to be well noted.Linear and non-linear relationships - Part 1 - Review of coordinate geometry
In fact, a number of phenomena were thought to be linear but later scientists realized that this was only true as an approximation. Consider special theory of relativity that redefined our perceptions of space and time.
It gives the full non-linear relationship between variables.
They can very well be approximated to be linear in Newtonian mechanics as a first approximation at lower speeds. If you consider momentum, in Newtonian mechanics it is linearly dependent on velocity.
If you double the velocity, the momentum will double. However, at speeds approaching those of light, this becomes a highly non-linear relationship.