I see, thank you. I was just looking at the method of linearizing where you take the partial derivative of every variable and noticed that you wouldn't have any constants left doing this.BvU said:Hey guy, no.
The derivative gives you the slope of a linear approximation. (in this case 2x).
A constant is still needed for the approximation in a particular point; e.g. if x = 3 the slope is 6 and the line has to go through the point (3,12), so a linear approximation there is y = 6x - 6 (or, if you want: (y-12) = 6 (x-3) )
The small angle method is a technique used to linearize non-linear equations by approximating them as linear equations that are valid for small angles. It is commonly used in physics and engineering to simplify complex equations and make them easier to solve.
The small angle method works by assuming that for small angles, the sine and tangent functions can be approximated as the angle itself. This allows non-linear equations to be rewritten in a linear form, making them easier to solve.
The small angle method is applicable when the angle of the system being studied is very small, typically less than 10 degrees. This is because the approximations made in the method become less accurate for larger angles.
The small angle method allows non-linear equations to be simplified and solved using techniques from linear algebra, which is often easier and more efficient. It also provides a good approximation for small angles and can give insights into the behavior of a system.
Yes, the small angle method is only applicable for small angles and becomes less accurate for larger angles. It also may not be suitable for all types of non-linear equations and may not give exact solutions. In some cases, more precise techniques may be required.