Bu ders doğrusal cebir ikili dizinin birincisidir. Doğrusal uzaylar kavramı, doğrusal işlemciler, matris gösterimleri ve denklem sistemlerinin hesaplanabilmesi için temel araçlar vb. konuları içermektedir. Ders gerçek yaşamdan gelen uygulamaları da tanıtmaya önem veren “içerikli yaklaşımla” tasarlanmıştır. Bölümler: Bölüm 1: Doğrusal Cebirin Matematikdeki Yeri ve Kapsamı Bölüm 2: Düzlemdeki Vektörlerin Öğrettikleri Bölüm 3: İki Bilinmeyenli Denklemlerin Öğrettikleri Bölüm 4: Doğrusal Uzaylar Bölüm 5: Fonksiyon Uzayları ve Fourier Serileri Bölüm 6: Doğrusal İşlemciler ve Dönüşümler Bölüm 7: Doğrusal İşlemcilerden Matrislere Geçiş Bölüm 8: Matris İşlemleri ----------- This is the first of the sequence of two courses. It develops the fundamental concepts in linear spaces, linear operators, matrix representations and basic tools for calculations with systems of equations. The course is designed with a “content based” emphasis, answering the “why” and “where“ of the topics, as much as the traditional “what” and “how” leading to “definitions” and “proofs”. Chapters: Chapter 1: Place and Contents of Linear Algebra Cebirin Chapter 2: Learning From Vectors in the Plane Chapter 3: Learning From Equations For Two Unknowns Chapter 4: Linear Spaces Chapter 5: Function Spaces and Fourier Series Chapter 6: Linear Operators and Transformations Chapter 7: From Linear Operators to Matrices Chapter 8: Matrix Operations ----------- Kaynak: Attila Aşkar, “Doğrusal cebir”. Bu kitap dört ciltlik dizinin üçüncü cildidir. Dizinin diğer kitapları Cilt 1 “Tek değişkenli fonksiyonlarda türev ve entegral”, Cilt 2: "Çok değişkenli fonksiyonlarda türev ve entegral" ve Cilt 4: “Diferansiyel denklemler” dir. Source: Attila Aşkar, Linear Algebra, Volume 3 of the set of Vol1: Calculus of Single Variable Functions, Volume 2: Calculus of Multivariable Functions and Volume 4: Differential Equations.
Çözümlü Problemler 3 ve 4: Fourier Katsayıları Fonksiyonu ve Ters Problem / Solved Problem 3 & 4: Fourier Series Coefficients and Inverse Problems
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Fonksiyon Uzayları ve Fourier Serileri / Function Spaces and Fourier Series
Ministrado por
Attila Aşkar
Prof. Dr.
[BOŞ_SES] Hello.
The previous two examples, was the weight calculation.
Here is how the series converges,
We tried to understand my representation of these four different relationships between them.
We will do the calculation, but the Fourier
What kind of work is done with the series,
perhaps showing the life of an application
I hope that optimistic creates excitement.
The first two forms of a machine part
It shows the vibration, one over time
öbürkü also shows the coefficients of the Fourier series.
This comes against equivalent representation in the frequency of physical space.
Here we look at a first
the vibration of the machine part,
teaching in this faculty of our university machines
members from Mr. Silk Özdoğan bought from Başdoğan.
The results of an experiment conducted onsite.
Here's something you do not understand well, we see such a random oscillation.
But when we look at it the Fourier coefficients,
in fact, we have drawn the previous cases and their Fourier coefficients
We understand that the show function.
This shows a sense immediately.
This part shows critical resonant frequencies of the machine.
This is an important thing achieved a great deal.
Resonance is desirable in some cases, in some cases prompted necessarily to be avoided.
Into the subject to its mechanical dimensions Us
but here there is no need to record how regularly appears this higgledy-piggledy
We see a structure, and this structure has brought very important information removed.
There's a logarithmic scale that increases are much higher here than care
so they are going to frequency means
no noise, ultimately, in terms of emissions.
The latter molecule's infrared
or measuring the release of the Raman method.
As you know, there are emissions of each of the free molecule.
What's also important to look at each item in Space
When you want to see if this kind of space in your gözlüyos emissions.
This is again a random oscillations.
Here it's not possible to make much sense, but Fury
take you draw the transformation and Fourier coefficients
When you see that there is great value in the base point.
Here, each of which also shows the specific frequency.
Drawings within this time.
This is happening in the frequency domain Fourier coefficients
It also shows the energy value.
Perhaps you can deal with the physics here, but it will be removed
the following meanings.
Higgledy-piggledy a record of appearing very meaningful,
simple, it can be shown a gain open to interpretation.
They also show some other Fourier coefficients I
such as the drawing is obtained.
Here 'hello,
Welcome to 'say hello to the sentence here has a break,
here in your lovely singing voice recording geldii made.
A record of that time.
As you can see from here on we can not say anything back.
If I removed Fourier coefficients from here I say it over the phone.
These appear below the Fourier coefficients of details that do not matter
for us.
Important of these,
This can be removed from the Fourier coefficients Fourier coefficients are counted.
These analog phone you're sending the vibrations of my voice.
In the physics lab we would do well even as a child.
You tied a rope to the end of a matchbox.
Here's nobody hears your voice or talked opposite the railway
If you put your ear you can tell the train coming.
These analogs can acquire the perception here is their Fourier coefficients,
Fourier coefficients also important here to know that it can be removed.
How have these ready software has been removed and that there is very
You should also consider can be done quickly.
If I were talking on the phone because I'm talking here hello welcome
When we say that returning to the fast Fourier coefficients.
They counted the number one team going.
The number for the numbers to no alteration.
However, analogue transmission, sound a little perturbation also suffers.
How very far gone as deterioration of the quality of the sound.
Fourier them again on the other side of this issue but to go with the number
coefficients are you able to build sound because it is certain.
This would be a living example.
But also the fact that television is made in two sizes.
But the essence of Fourier series, but useful in this technology
It has to be at work that can be done quickly to this fast Fourier transform,
We also FFT fast Fourier transform is obtained from there.
I hope some excitement with them a hope
You've heard it because we live in a technology revolution hakkaten serious.
Contact, recording CDs, DVDs.
Thousands of pages a little something to compress all this digital
Thanks to technology transformation lot of time to learn it
I also want to give you an example of an inverse want to ask a question like this.
It's a function from the Let no account of a reset for example,
Fourier coefficients directly without my direct access I could find söyleyebilel
As an example, I can see this as follows
function and if you three times cosine of pi x 10 x minus twice sinus 16,
do you think that you two cosine pi x
sinus was opened in two pi is a series of x base.
This is a five three coefficients considering the two factors.
The B minus eight is two.
So here is no need to make any calculations.
Whether you take the integral t account already you will find here the coefficients.
Let's do an example.
As you are given a function.
We want to turn this function Fourier series.
One way to get hit with a series of cosine sine with it.
There are other ways cosine sine here and all of them are here since two sine pi x
cosine of pi consists of two numbers, such as x, we can look to their expansion.
Sine square p x, as seen here at work in terms of double formula
When we hit them again will be a sine terms a
multiplied by the cosine and sine it will be.
We know the identity of its expansion from this trigonometik.
This can bring it fully into line with the algebraic method.
Here eight sine pi x 10 pin x 12 pin x,
14 pi x 16 pin x number of turns, back to zero.
Here we find that the coefficients immediately.
This inverse problem here, because here we know just the Fourier coefficients.
We also do it now drawing to drawing functions.
It also reminds you can immediately see where this little thing.
There is a big factor, they have a small coefficients.
I'm just gonna draw this thing take this large number of times,
Show what the function or taking all factors.
See the first two alsam quite a nice big factor approach
I'll get.
Here produced by the two terms here all
It was produced by all of the three terms.
A well designed with two customers, there is little sense of a grain,
but the two terms, ternary and fourth coefficients are already zero,
Taking in the fifth coefficient then is the ultimate solution.
Comparing them.
As you can see large coefficients,
Taking the large number of times I can get quite a few good approach.
This gives you an idea of my voice on the phone such as transporting
Or, TV transporting Or,
while trying to find the release of a molecule,
I take the large Fourier coefficients, öbürkü Maybe I down a
I get so considered approximate values.
This gives it a context information.
Now, as the basis of transactions.
Fast, calculated with the Fast Fourier coefficients.
The integration is done.
I suggest you read here.
These advantages, such as math, rather than what they practice,
What kind of contribution can tell that bring high technology.
Issues such as CDs and DVDs with audio recording and so on, of course anafikir thereof
that they learn important technical issues per individual.
Now here we see the good side of all of Fourier series.
There may be some difficulties.
If the FUNCTIONS discontinuities, thus we examined our pre
in this saws FUNCTIONS FUNCTIONS look at you there is a discontinuity,
FUNCTIONS there is a discontinuity in the box,
What's happening, we'll see what some of them have difficulties.
Convergence Is there Fourier series of each function,
How converges, what is the speed of convergence?
We will look at issues such as this.
These issues will also be the last, and so
We finish the part of Fourier series.
If we think from the beginning,
We choose a base function in linear space.
These functions are also orthogonal base which functions like sine and cosine.
There is nothing too much apart from that of j k
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