Well, I have a very strong background in natural sciences and engineering, and it is not a big building block. Very few derivations in physics rely on it for instance. I know this is -1 controversial, but I think the appeal comes from the ease of doing tricky questions based on it. Sort of ETS style questions.
A similar thing would be the vertical angle theorem or whatever it is called, where a line crosses a couple parallel lines is big on the SAT. And that in preference to being able to do multistep mechanical problems like a maximization or power series expansion.
Well symmetry helps investigate functions. It's the first things I need to know about the function I deal with. It helps as noted, evaluating integrals that are otherwise difficult to integrate. And it helps visualizing functions. I was a bit disapointed by the few examples given in class ass aplications of these concepts.
When manipulating and equation that contained Cos -x we are able to observe that this term is the same as Cos x. On the other hand, when we see Sin -x and want to manipulate to form a positive argument, it's equal to -Sin x. I don't feel that we spend that much time on the concept. It's introduced in algebra, a parabola possibly being even, a third degree possibly odd, and then again in Trig with the examples I gave. Your experience may be different, more focus than I've observed.
Learning mathematics isn't always about applying things to further mathematics - it can also be about actually applying that knowledge to other areas. So let me bring you a completely different answer to your question, coming from the background of someone that does programming and some web design. A simple enough requirement, that a good programmer might understand not only on the surface, but more deeply such as yourself.
I apologize if this answer is not relevant to the mathematics community directly, but I felt the need seeing this question in a suggested list to remind people that math isn't just about math ;. Sign up to join this community.
The best answers are voted up and rise to the top. Examples of even functions are x 2 , x 4 , cos x , and cosh x. Again, let f x be a real -valued function of a real variable. Then f is odd if the following equation holds for all real x :. Geometrically, an odd function is symmetric with respect to the origin , meaning that its graph remains unchanged after rotation of degrees about the origin. In particular we get. This is what we defined at the beginning, so it is true that the product of two even functions is an odd function.
Article objectives The purpose of this article is to introduce the reader to even and odd functions and their significance. Introduction Even and odd functions have significance in graphical analysis, especially of trigonometric functions. Even Functions Here is a basic example to illustrate the properties of even functions.
The cosine function is an even function; it is symmetric relative to the y-axis. In mathematics , even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis , especially the theory of power series and Fourier series.
Let f x be a real -valued function of a real variable. Then f is even if the following equation holds for all real x :. Geometrically, an even function is symmetric with respect to the y -axis, meaning that its graph remains unchanged after reflection about the y -axis.
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