Working with Complex Numbers

The first known reference to square roots of negative numbers comes from the work of Greek mathematicians such as Heron of Alexandria in the first century BC, as a result of an impossible section of a pyramid.

Since then,throughout history was perfected this technique thanks to mathematical people such as Cardano, Euler or Gauss...giving us the Number Complex science we have nowadays.

An imaginary number is a square root of a nonpositive actual number. Imaginary numbers Have the form bi where b is a real number and i is the imaginary unit, defined as the square root of -1.

An imaginary number bi can be added to a real number a to form a complex numberof the form a+bi, where a and b are called respectively, the "real part" and the "imaginary part" of the complex number. Imaginary numbers can therefore be thought of as complex numbers where the real part is zero, and vice versa.

The name "imaginary number" was originally coined in the seventeenth century as a derogatory term as such numbers were regarded by some as fictitious or useless, but today they have essential, concrete applications in a variety of scientific and related areas.

                                        

Let's talk to someone!

For this post, I did an interview to a friend of mine. His name is Manuel López and he is an Industrial & Engineer Chemistry, now tuttoring professor by his own.

Q: Why you decided to study an engineering?
A: Well, I always wanted to study an engineering because I really good at Maths and Chemistry. Also, my mum was a Chemistry teacher in a school and he helped and teached me since I was a chilld, thus motivated me definitely to study it.

Q: Did you find difficult the degree? Tell me some experiences
A: All engineerings are difficult and requires a big effort. In my Freshman year, I failed several subjets and I've been far below my capabilities. I tought postponing for the time being, but then I thought better and I was concerned about it...but then I decided to continue. Freshman year are the most difficult for me. Universities as a rule make a sieve to select between good and bad students...Fortunately I pass to my second year degree only with 1 subject failed.


Q: Do you think, nowadays engineerings are useful to find a job?
A: To have an engineering degree always is a plus is your curriculum. Engineerings are hard, somehow requires a strong knowledge...But, it's known that now things are difficult...and the "crisis" also affects engineers. After finishing my degree I had to wait 2 years to find a job...in an office!! I've never though to work there studing an engineering...


Q: You have a hard degree, but now you are a tuttoring professor...do you like your job? What are your job expectations?
A: Well now I'm teaching childs and secondary students in the scientific framework. This is not what I want, but now things are really bad...Actually I like to teach, but I always wanted to work in a central nuclear or something like that...I have already take a look for some jobs, but it didn't call me yet. I expect for a enhance situation!

Q: What advices would you give to an engineering student or someone who wants to study an engineering?
A: Never fall, do not be discouraged and fight for it's dreams...They have to find several obstacles in his lives...but all is needed to learn. It's important also to have a high english level, and also travel, travel a lot...specially in first years! It's importante to widen your knowledge as far as possible.


                                   

How to learn integration? Why do we need to study it?

Hi! In this post I'll be talking about how to encourage easily integration
The best mathematical knowledge is to assimilate concepts in own pace. Integratrion is one of the most importantes operations in the integral Calculus. Actually, it's the reverse process of differentation in the calculation of areas and volumes of irregulars shapes and solids the integration is used.

But, why we need to study integration?
Often we know the relationship involving the rate of change of two variables, but also we have to know those direct relationship between thes variables. For example, in Physics, we know the velocity of certain object at a particular time, but we want to know the position of the object at that time too.
To calculate this direct relationship, we need to use the process which is opposite to differentation, called integration.
The processes of integration are used in many applications and it's involved in so many frameworks. As an example, the Petronas Towers in Kuala Lumpur have to bear high forces due to winds. Integration was used to design the building for strength.

Here you have an interesting video if you are interested on

 http://www.youtube.com/watch?v=J3CQ1bmEX9Q  Enjoy it!

The advancing of Maths

Nowadays, maths are used through the world as a essential tool in many fields, such as natural sciences, engineering, medicine and the sociel science, and even disciplines that apparently are not linked with it, for example the music.
Mathematical knowledge of the modern world is moving faster than ever. Some theories that were completely different, now come together to form complete and abstract theories. Although most major issues have been resolved, others like Riemann hypothesis remain unresolved.
At the same time, it still growing new problems. It seems even the most abstract maths, are finding new applications.

What is calculus and why do we study it?

Calculus is the study of how things change. It provides a framework for modeling systems in which there is a change, and a way to deduce predictions of such models.

But why calculus is so complicated? It they require concentration and reasoning, therefore we must teach with patience, clarity, dynamics without isolate the contents of children's everyday life. But the big problem of this matter is that small often stereotyped from small child as "good" or "bad" at calculus. And the "bad" are left with that taste bitter, rejecting them forever. According to her, the solution is to help children develop logical thinking in preschool stage, but also teach foundations when we are child.

Sometimes we tend to wondering why we have to study calculus, for example to be an engineer, architects or even militaries...if at the time to work, we don't have to solve integrals and so on...why?
Well, calculus, is in all. Sciences often rely on mathematics and calculus  to articulate their findings and predictions. Colleges and universities should give an extra focus in this aspect, to involve people to learn calculus.

"We are all a variable mathematics. Behind it all, you can set a number"

About myself

Hi everyone! I'm Iván Lage and I am a student of aerospace engineering in the Universidad Europea de Madrid.
I create this blog to tell you what we do in the class of Calculus I. For it, I will write several post per week...I expect you enjoy it!