Hi there. With you the most important heritage of mankind In one of the topics of this civilization engaged in one of the foundation stones We're going on a journey of seven weeks. Each lesson is a communication issue. Contact the following basic questions. We want to define an event. What we asked. How did it happen? Why is that? Where and by whom he. Mathematics is a subject of communication. Each lesson answers to these questions as wants to give. In general, the identification of what a thing shows. How to answer in math proofs solutions shows how it's done. Why so often in mathematics and even avoided a lot of space to respond issue. The reason is because sometimes the answer is deeper but the subject thoroughly To understand why we're doing this work we will respond. Where our findings are used, We will also examine where they come from. Who several times by the may bring an additional contribution. Now with you a cultural E, accumulation of this course is to provide general where between the mathematics courses I want to start to describe that. Higher mathematics at the university infrastructure consists of four courses. You need to move to the country in which similar infrastructure comprises. First lesson univariate functions occurs. E thereof, the most important derivative integrated issues. The second course of several variables are functions. We learned our lesson here is shown in dark The second lesson like this. To take the next course, of s linear There algebra and differential equations is there. All of these are shown separately in the fact that the relationship between them has not. Just a lot of lessons univariate variable Let us emphasize the difference. So much so that even your course before starting school y is equal to x for x as the independent variable x to y this Depending on the numeric changing Have you seen functions. Here you can see where y is the generalization y as a, y two, that there is a multitude of components, such as y m situation. A similar gene in X, x, x two, x is composed of many variables, such as the will deal with the types of functions. With this generalized univariate functions we have seen in basic, fundamental issues here will be used. As you tour again with a wide horizon I want to start. I hope that in the coming years to 20 years later, After successful people in your profession is many will forget the formula. But the culture will remain. Therefore, what is this math a little bit about E, you think of a future deep, will be enriched. Instead of answering this, what mathematics process that makes it easier to identify. Mathematics is a communication tool. A language and a culture and strategy. In the sense that language. Judging Current language language elements, items consisted of words. Using the rules of grammar and We are using logic sentences. This is our statement of our observations Sentiments and all of our transfers bringing a sense of life, to understand life observations employee's happening. This life is real life connections fictional world as possible. When we came to mathematics in mathematics A very similar structure. Mathematics defines the elements of the same this equivalent of words. You can not question the rules of grammar. That the rules of Turkish grammar other grammar of the languages themselves based on. Please ediyos accept them. Accepted without question in Mathematics 've got concepts. We call these propositions or axioms or in Turkish, also called postulates. Yet in the same way as in the language of logic with rules to generate sentences rather than in their sentences, sentences We produce anti-math solutions. Our observations with them, We're sending our thoughts. Our subject in real-life still life still We are trying to understand the issues or issues now we do not know To reach fictions are doing. Sometimes they may be wrong. But this, again, uh, what we know environment to learn the language we use mathematics. To begin with, a transfer from Gallien here I want. Biliyosunuz the world's solar Galilee revolves around the scientist said. 15, century. Galilei says:nature's book, perhaps It is written in the secret language of mathematics. Thus nature, we produce here technology, we have produced here humane science to understand this statement, language major holds a place. He would like to talk about a cycle. This is our topic in current language of mathematics language that is converted to if b is a translation from the language into another language as such. First, we have bi observation. We know that verbal expression. This is the logic of verbal expression language, mathematics 're doing language translation. Mourning the end of this translation, the same problem We find the mathematical expression. These are usually in the form of equations is going on. Peculiar logic of mathematics rules derived from solution of these equations to methods We solve and initial obtain the solution of the problem in the language of mathematics We are. This is because we can not stop here mathematics everyone again in the language of expression We need to return a language that can be understood. So here's the current language on the language of mathematics We have turned. In contrast, this time from the date the language of mathematics We are translating language. Thus, in the language of mathematics solution from the expression We arrive in the current language, verbal expression. Does this answer is always meaningful iii need to check that. Otherwise we incorrectly useful and b Google has undergone We could not find the answer to that observed would be. There are such a cycle and the current language e of mathematics, the cycle and again starting from one to the other the current language, we're going to live. Living and mathematics Did you, I said. What we can think of the elements of life. On the basis of what life is made up of? There are objects in life. Knowing the amount of these objects we want. We want to know the format. We want to know the relationships between them. And some of these changes and at the end of We observe formations. Mathematics responding to this question the branches are as follows:Object of the In order to quantify with numbers Our arithmetic means dealing going on. That defines the format, try to understand The branch geometry is happening. This relationship between objects algebra determine the branch. The number of arithmetic means in ancient Greek. Means to measure the geometry of the world. Geo in geography from the same word. Geology from the same word, from the origin. Algebra editing the Arabic origin is coming. So what is it to understand the relationship regularly obtained these relations to. To examine these changes and the formation of tools that help in the analysis of call. What are the tools of mathematics that works In order to do? Since first grade mathematics perhaps even we saw earlier, the four process is there. Addition, subtraction, multiplication, division. Already these are interconnected. Removing the reverse acquisition, multiplication, successive collect for example, five times the same means quintuplicate number of means to collect himself. Dividing the inverse of multiplication. We know them. Did you see the part in high school. There is an important issue. This infinitely small and infinitely large with Taking these limits so our vehicles. Subject's name. This has always been a problem, actually. Our topic for the following terms are used. Higher mathematics, analysis, analysis geometry together. Recently, a little American culture, from the Anglo-Saxon terminology the calculus. Differential calculus and its By combining analytical geometry used together. If you prefer the name you I have stayed. But it also brings a sense of all. High math says now. Earlier than you can see the math You will see an advanced topic. For example, in the anatomy of the analysis under the same There are words. Dividing the lower parts descend understand understanding, in the sense of Liz to loosen. To divide into sub-components, such as loosening the word comes from. Calculus, this is very interesting, stone, gravel, stone comes from. In the past people to make accounts gravel They were using stones. As you know, then you as a child You have to play with beads On a small table called abacus accounts was made. This calculus with pebbles account construction of the historical origins of the reports. We use in Turkish limestone, calcium comes from the same root. The difference calculus differential calculus. The infinitesimal differences differences. And here we'll see. Likely to have seen before. Limits will be important. Perhaps the most fundamental observations in life changes and formations. Showing the formation of an accumulation. Changes show a difference. Change a difference. Wherein represents the difference mathematical operation subtraction and division operations. You can also find the difference between a thing. Referring to the ratio between the difference Do you understand. This splitting process that will see us derivatives business, is taking the concept of derivative. Many applications of derivatives. Velocity gradient in the geographical sense, ups and downs, descent of the temperature of a patient to exit the stock market's ups and downs figure is based on all the differences. B shows the accumulation of formation. Accumulation at mathematical operations that collection and diameter. Accumulation have collected shows two things. If you get the same thing five times, the shock process, it shows bi accumulation. This shows the basic integrally. As you can see it is derivative and integral Or not at all miraculous mysterious terms not. Of arithmetic operations thereof in accordance use is made of. This accumulation also in the physical sense, for example The accumulation of work it would be doing anything. In physics you've seen. Article accumulate accumulate, mountains, seas occurs. In fact, the accumulation of financial resources from the financial issues occur. All of them consist of integrals. So you have two main tasks in life. Change and development. Two of these four operations extraction and compartment leads to derivative transactions. That describes the accumulation of addition and multiplication leads to the integral. So many miraculous legend, a mythical topics we will not. This course alone to measure variability and Analysis of the most significant, differential calculus to the most important, element of the In addition to these four operations Limits. As things have limits. There are infinitesimal goes to zero. As the equivalent of one infinitesimal If you divide this time its the limit goes to infinity. In this respect, some infinitesimal way to zero things can go forever. Our subject to the following three, eg, lower housing consists of: Derivatives, the series has integral bi. We will see in series connected them immediately. As derivatives. A function of the value of x is zero From this value is around dividing this difference that takes arguments We find the slope of the function. In this univariate function Did you see. This honor us, leads to derivatives. Please note alone, xa xa zero and uncertainties, such as zero divided by zero if occurs. That requires limit these derivatives Here comes the process. Zero divided by zero is uncertain. This is to remove the uncertainty of human intelligence, perhaps close to the 20th century found that by spending a period of time, it has developed this limit vehicle concept. Similarly, the bottom of a function space If you want to find it again, only Did you see the variable. Function next to the value of two small the difference between la, b by multiplying the rectangle We find the area. By collecting area of this rectangle the this under the curve, the area we find. See it here x go to zero n is the number of parts. This also goes to infinity n. f x k in it s also no longer discrete spots becomes continuous. In the limit when it has We arrive to the concept of integration. The derivative used in the d's Western words in the languages of the differential d the letter is coming from. This form of the gene of this integral Sum in Western languages to zoom in German the word comes from. Because it's built, people in this country first for their contributions to their established accepted terms. It s an extension letter from the pull occurs. Infinite series of the differential calculus part. Here's the thing. Get one of the differences between this x. Then this will be deducted from the total. The total numbers than ever I might. Because the values of the function x k will give you a number. Such functions to work from kolaylat abandon them, by definition, K If we say that there is an infinite series where We want to find. Of course infinitely many terms have collected infinity There can be but there is a finite We know. Here our subject is made up of them. These multivariate functions for generalization occurs. Now we need our prior knowledge. Çüök, multivariate functions To be able to single basic knowledge of multivariate functions You need to have. Using them as e, our lesson As issues occur. Course, in the first section necessary preliminary information about the nature and I will introduce. And also, vectors, lines and We'll talk about the plane. Because more than one number by vectors the name given to the extent defined. Therefore multivariate in function of the independent variable x and the dependent variable y to understand vectors are needed. Also important vectors of its own. For this reason, in these vectors lacking If you are sending information. If you are missing in order to complete well as a chance. On its own, thus the vectors b the purpose. But it will also be used as a tool in this course. Verifies the simplest functions. Planes of multivariate functions The simplest types. After this general introduction univariate We will work with vector functions. So while this x is a vector y b, x two, x to n of the variables that can go up only One to function as usual vector functions is saying the call. With these emerging space curves. Then the dependent variable y is an odd number so that there is a vector y, y two, as y just one year When it occurs, but at least x and y of x such as from two variable When it occurs, the functions of digital earliest onset of functions. Here are two variable functions we see. Just after seeing it three and n variables to generalize the concept Do not say but it is an extremely simple Siya b can be easily reached. All of these derivatives and integrals in descriptions and some applications We'll see. After making their numerical applications of derivatives of functions We'll see. Watching it now at numerical integration of functions We will see applications. To our subject, but with the construction, infrastructure formed happening. There then vector fields. This vector fields di, di, usually physical quantities such as an electrical area, Or a heat flow, a gas, gas, liquid shows a size as current. x, y, z position in the space, the space of the inn, At what point is it is worth? t at time t indicating the time in space x, y, z at the point of electric field of a fluid flow field, a heat, heat to flow, to see the value of their is required. In order to facilitate this course approach We give two components. The first seven weeks of the basics of this subject We'll see. Because these advanced techniques before entering on the basis of the most basic concepts I need to understand. After seeing this, the second of seven weekly If those who wish to take the course, with this more comprehensive applications and more We will see a comprehensive method of calculation. How should I follow this course a recommendation I want to make. Bi to the extent capable of times each week course to gidermişçe regularly to listen to this program I would recommend. An audible and visual If you listen to. Meanwhile perhaps have the opportunity to take notes may not be. But we repair these modules a small min We give near as modules. After that, surely you do not understand will be. If you already understand all of this course is very air-water course is bi. Do not understand where you will be. A second look, listen, the examination figure out where you stand, especially in Seeing your progress. A second course of rapid eye If you spend. Every week we will give you homework. I suggest making these assignments. These papers make it easy for you to Each a way to display and responses will be given. Therefore, to make transactions between them to be expected. Order to make it easily similar There are plenty of such examples in the parsed. After doing them in making assignments difficulty should not. A summary section at the end of each lesson will provide. I will not present it here, but this summary portion, of the main topics in Your own ability to test your level of understanding will be. Now of course have the following question. Are you ready for this course? The front of this course, as a single infrastructure You need to know the variable functions. But I do not know this one will be. Even to take this course last time may have been forgotten in. This is a good opportunity because it is so variable in function 95 percent of all issues Provision of functions of one variable is there. Therefore, before you start any threads functions of one variable in their What's the opposite of what was to investigate I'll start. Therefore, the only variable functions If you are aware of them to remember, for your practice I think a good opportunity.
