We briefly with the concept of the four functions I want to say. Function between the elements of two sets relationship. Euler gave this definition for the first time. Euler's name in many places 've seen. Co-founder of the foundations of mathematics today. In 1748. So time passed more than 250 years. But after an interval of 100 years, but today we accept the function given the definition of the Dirichlet. Euler, a Swiss scientist and many scientists in the family disconnected. If the Dirichlet German. In every single function of x against only one year should be. But the opposite is not necessary. So for each e y must have a single x it is not. But it comes to y if x is a single this a special occasion. Which is preferred in some respects, the desired a situation. A call to this function. Let's take an example. Current quad was a printing error. X squared plus y squared equals one know a the equation of the circle. If we take the square root of y taking it two because one equation we obtain where each x opposed to two years means. As you can see in this figure plus This marked the top semi-circle, with the minus sign at the bottom semi-circle shows. But they are each a function of it is not. This representation of a function. Four x in each one, but four to this function for years to come opposite does not meet the definition. But each of these functions to the definition of fits. Because for every x, we find a single year. you'll find here all x for y years. The one you here. The one you here. Two different functions. Here you have two equivalent with the function This function means. But this is not a one to one function because each As you can see the value of x for y two is there. This was a subject I want to remind you again. Finally, functions, duties I want to introduce. A function of a machine can be compared. You're giving an x inside. This machine processes the team is doing b give out at the end of the year. This x is an odd number of years a This is the number one single variable functions i.e., a vector consisting of a plurality of sizes so that from the number of this consists of a very büyüklüks variable functions are happening. A second function of the display pattern that We call the representation. F is an xu. X is an example taken here. Y contrast, the finds. Xi is yet another contrast find the y. Up and down again like this, but this this term is used to shipping. Turkish ships to mean the function s are using. A third form of bi numbers table. X can take values. Receive from the opposite this year. This is a function even if you çizmese show. Because here at any time Do you find it. But such an axis to bring them If you show here is a simple curve This comes here to have taken the value of x that x value of coming here. Between this point and mark a continuous By combining the function obtained by the line Do you have going on. Gene conversion as the last one in your hand The one thing to something else transforms. Here, perhaps you might be interested in work from the sad drama and theater icon comedy transformation. They are all doing the same thing anyway. Here, too, take x an y transforms. Y, where x is the bears. As such, all doing similar things, but The small differences between these as we see. There are four basic structure of functions. Where we want to go I repeat very variable and highly variable one and only one X only If more than one year lags somewhat behind the univariate numerical function call. This is opposed to a curve in the plane is coming. If there is only one x one I mentioned but a number of years If you are experiencing this vector univariate function call. Easy to get the impression that instead of y x, x instead In this space, mostly because the t call shows a trajectory. T indicates the time. X, X, Y, Z coordinates comprising indicates the position. This comes opposed to a curve in space. Yet this time the opposite, similar where x has an odd number oluşuyo than a year consisted of a single number, but more than x it is made up of the number of bivariate numerical function is called. Wherein the gene to facilitate writing with one or two indicators z where x instead of y to deal it has to be at least two numbers. Both x and y instead of x means that X is a call. After seeing these two variables to three and in general the libitum number of functions is not difficult to generalize concepts. Of course accounts are confused by him. We're also a little feature vector field is there. We're also here instead of y. Because of this physical quantity To say that show. In this context, we have shown for X, x, y, z and t is a vector comprising location. As I often say that u physics elements or elements may be in the economy. This means that such vectors. So overall number of multivariate fonkso, functions Before examining the f's in the most general the linear function structure is very important applications g provides. So it's possible that a linear function f means x1 x2 xj only the first force of XII to be found. Therefore, when we wrote it each y for y component Y1 Y2 has he. Each of x only linear function will be. That is one of the sine of x to x is a square tops will not function. These types of functions occurs. This functions as the coefficients a When the knee in the table it is called the matrix, and this is what concerns us it is not. Although multivariate functions While it is a special structure without the need for this analysis concepts algebra concepts will be able to see the job through. This is called linear algebra. I have previously described this linear algebra From these four courses, one variable functions, functions of several variables, linear algebra and these four basic equations were lesson. Third of them. This is not our concern in this context. I want to tell the types of functions. Types of functions between x and z to show the relationship. However we look around our dependent variable x, y independent clear indication that the function variables We say it's our deficit. However, in some cases, x, y, z along found. If you remember the equation of the circle only Although variable functions of x, but x squared plus y y was you wrote squared minus one equals 0 If this is a closed function of time representation is happening. As it can show in general. X is a vector. Wherein x is a vector. So x1, x2, xn can. Here x1, x2, xn can. I have also shown that a parametric When you look here z is equal to x when y x's and y's fonksiyonuyk has two degrees of freedom. These two degrees of freedom direct with x and y to correct where x is to provide indirect u and v are themselves the two variable quantities expressed in We can. Z Y so too. This is variable to distinguish it from and v the fact that they but separate from where the x and y variables to highlight that the these are called parameters. It's called a parametric representation. If we write this, a vector x of tidy components x, y, z, u and v as a vector We show. BI vector function is happening. In the plane of single variable functions I want to give an example. BI equation of circle saw. This is equal to the square of the circle from the equation y We can solve x squared minus. Similarly, x instead of theta parameters xi denominated y y again in terms of the theta parameters we can express. Wherein the position of a point r in length projection of x on the x axis y axis projection on the I think y r times cosine theta will x and y r times the sine of theta would be We know. This parametric representation is happening. Here are three we are treated. Off function representation, the open function representation and parametric functions representation. Similarly, a bit more complicated this Consider the equation of the sphere. Implicit function representation of the sphere x squared plus y squared plus z squared minus a squared equals zero happens. Here we can solve z. But as a function of X and Y is We also know the geography latitude and longitude angles theta and file to be referred to in terms of the two variables We can. I do not want to go into detail here. You will find simple geometry. This mesa, you get the size of the projection time in the state where the x-y plane We know. Located in an email that you just reminders I say this as than with spherical coordinate future will encounter. Now here you will handle issues mathematics Where I work at, attend shows that a little to the cultural What to tell the size of mathematics What is understand what works, to describe some information was transferred. Now here later this bet off What I want to say that the subject. As I said in the future longitudinal single Some of the basic variable functions Our knowledge is supposed to be. This course is to understand, monitor and In order to be successful. He details the preparation of this course in terms of bi Our next session will tell you. Bi goodbye until more opinions.