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Hello, with you

We begin with a topic will take 10 hours.

This is our journey, our Linear Algebra class.

In this lesson, we're in two parts.

First, the basic concept: What is Doğrusalık?

What is clear linear spaces and linear processors?

We're starting to recognize that.

As at the end of the matrix of the linear processor, the number of directories,

two-dimensional yellow, bring the number of representations as directories.

In the second part, in particular identifying the privilege of square matrix

We will see how the calculation methods and practices with them.

Part 1 also a journey time of 10 hours, in Part 2.

But everyone has their own knowledge of them

According perhaps has information about Part 1, it can directly start in Section 2.

These two components were done independently.

At the beginning of Part 2 Part 1 There is also a detailed summary,

information for those who want to complete.

Now read Chapter 1: Linear

We begin by presenting the location and description of the algebra.

We are doing a general tour of the horizon.

Higher mathematics in the university infrastructure

especially in science and engineering education who

There are four basic courses for.

These single variable functions and their derivatives and

integrals and infinite series in particular.

Subsequent multivariate functions.

These are the same issues, derivatives and integrals and series

but generalizing to multivariate functions.

This lesson is written in bold letters Linear Algebra.

These two courses administered independently.

Last course in differential equations,

Topics of this course is now crowning infrastructure.

As we begin to multivariate functions.

y = f (x) from one independent variable

dependent variable "f" function we get through.

If that x is not a single number in the grain

The number of independent variables such as set here so

n consists of many, many years if the dependent m composed of variable,

this single variable functions becomes multivariate function.

We can connect it to the emergence of linear algebra.

If this multivariate functions are functions that relationship,

the relationship between x and y, this relationship only x 1.

If so it consists of force y1, y2, ym each of x1,

x2, XJ, xn'n the only one.

içeriyos to force the sinus of another function, cosine,

This relationship does not contain an exponential function is determined by a number of coefficients.

This relationship as well as more compact can show such a collection.

That is a, i, j constitute a matrix.

The final destination of linear algebra,

to perform operations with the array of numbers, to define the topics.

Let's do a tour d'horizon as he set off.

What is Mathematics?

Now there are many details to our math, but math

not just a calculation tool for a much wider communication tool.

In this context, a mathematical language.

Think communication is expressed by a formula

You can express full pages of the current language.

Very economic language.

This language is in itself a revealing flaws immediately

Thanks very effective language for that language and this language

already in the current language, the language we speak, we are doing it.

A culture, and that culture consists also consists of a series of strategy.

You have a given topic.

Furthermore you define the strategy to take an issue and that

It can be reached through the new information strategy.

To promote the similarity with language similar to the current language

Consider the following elements to.

Languages, consists of the word.

Objects, events,

bellirt properties consist of words.

These words and the grammar rules

We create sentences using logic.

The formation of sentences in our observations, we convey our thoughts.

so we are transferring life.

This life can be in real life or fictional life as a dream

It can be a tool for understanding our lives but our lives.

Mathematics as such.

Mathematics starts with the definition of the elements, such as words in the same language.

Grammar of Western languages as equal

Or, propositions, axioms or postulates with transfer through

We give thanks to new solutions and combining them with logic.

This, as we establish the same sentence and also with this solution

We convey our thoughts observation.

Our subject is still living our lives because of this observation,

but beyond that, real or imaginary fictional

There is also able to observation.

Galileo by saying I want to complete this page.

Galileo says: "The book of nature, perhaps secrets,

It is written in the language of mathematics. "Today the modern technology to understand,

To understand the natural sciences also need to learn this language.

Of course you have to start learning the language in the various classes.

We will deepen some topics that you know in part.

Naturally, we will learn some new issues.

The current language, the language of mathematics cycle may think: We have an observation.

Before that we find verbal expression.

We translate this verbal expression of the language of mathematics.

That one, a quality language translation from one language to another.

This kind of expression we have obtained new is happening in the equation.

We solve this equation.

This solution is a representation of the language of mathematics, it's the wording.

Here again makes an interpretation of the language of mathematics again

The answer to the language as a linguistic turn,

We find the answer we obtained verbal expression.

You should always make an effort to respond to the audit we found.

We found our way in response to observations

Does he developed and harmonized.

You look due to an error,

There can therefore result in an unreasonable assumptions.

Any translated, from Turkish to English

tecü with a bad result too bad when translated into Chinese

You can have the same problems here may also occur.

So the concept of mathematics is a language,

it is wise to know as a cultural achievement and we are going with such cycles.

Life consists of what?

Because we said we will explain our observations in the language of life.

It is composed of objects.

There are some of these bodies, and there forms

There are relationships between these bodies and consequently the life

emerging changes and formations.

There are various branches of mathematics in these relationships, these quantities,

This form of sub-branches and serves to explain these changes and formations.

We express the amount and number of arithmetic.

We define geometry formats.

Between these bodies, we mean the algebra relations between phenomena.

Change and development is expressed in the analysis.

We need more than anything because the analysis of this information.

What are our means?

In fact, we do not have too much to be an effective tool, but how much less this

Information on how large the transaction number,

We are able to obtain basic information can connect.

There are four operations.

We know the collection, and vice versa, subtract, multiply and divide the opposite.

Algebra, we will benefit from them.

In the analysis, of course, you can also analytical geometry,

You can combine them or something but,

Let's say that only a brave separation main structures.

These include the interaction a must.

Analysis endless dealing with small.

This ball, in addition to these four processing,

Taking derivatives and limits in this infinitesimal

integration or require us to find the limit of infinite series.

Linear algebra name of our subject.

Algebra is a branch can be made only with these four works.

In linear algebra who say there.

The English the "linear algebra" comes from.

Our topics as follows: We're talking about space, we will talk.

Vectors, transformation, matrices, equations,

He is interested in the topics of linear algebra.

Only four transactions in linear algebra enough.

Little can be done without the need for endless.

It does not require serious preparation

To understand linear algebra.

Looking at the comparative analysis of infinite sequences,

series, as derivative and integral and essential tool's four

it is also beyond the limits of the process we have already said a little while ago.

Knowing this structure, learn, internalize general

providing a culture I bring your attention.

We specify the location of our theme among these four courses of linear algebra.

All these courses are an end in itself.

But this, as well as differential equations that crowning these issues

a topic, a field.

Preparing them and used them as a tool.

We looked specifically linear algebra

When the matrix is used as an important tool

and today we are experiencing a serious revolution, the technological revolution.

This digital revolution, the digital revolution because the revolution we said,

This computer science, communications, and generally in digital

a branch holding the most important part of our success in linear algebra calculations.

You briefly our issues

present and then I want to shut this module.

Our subjects like this, already one of those, we finish one section.

It means the place of mathematics linear algebra, linear algebra

place in general mathematics, we have made a tour of the horizon.

Bunda has again after two preparatory department.

WILL learn from the vector in one of these planes.

You see this in many areas, you see the absolute in physics.

Maybe you work but also as vectors starting here

a large two-component vectors, not just generalities,

We also draw the biggest of the three-dimensional vector, and even impossible

We go to the infinite-dimensional function space will be possible.

However, although many still seem like a simple issue

We'll examine two variable equations drinking very foundations of the subject.

There are many things we can learn from it.

How do you know for sure, but at a fraction of their generalizations

that develops, that should lead to the idea of space,

linear function spaces and a series on the digital revolution's fury

is one of the areas where much advantage, how it came,

linear processor what it is and how to transition to the matrix here

These two simple as that provided all the visible area, the vector of the plane

and they will now teach the generalization of the equation with two unknowns.

Bunda I see the following benefits,

We can begin with a series of propositions completely linear algebra.

But then suddenly very much airborne and grip

starting with an abstraction that is difficult.

However, these vectors and two unknowns in the well plane

generalization of the issues contained in the equation.

Therefore, we keep them in our minds this transition as much fresh

I hope we can make it easier.

Bye now.