I am still actually working on the final part (Part 4) of HOW LEARNING CAN BE FUN. I am trying to end up the topic with an impact but frankly speaking, it is not easy. To finish what we have started is the most difficult part, isn't?
So to keep feeding this blog with material, I have decided to make this entry which is actually something that I have posted in an FB group called Dr Airil's Finite Element Forum. This forum was set up initially by a group of students who currently attending my class on FE. Now, this FB forum is opened for public. So herein, I like to invite the readers of this blog to join the forum by visiting
http://www.facebook.com/groups/244071082308340/Basically, in this forum, the students, members and visitors are free to ask me any questions about Finite Element Method and I will try to answer them the best I can. Please visit and become a member. Lets hope that this forum can be an alternative and interesting way for us to know more about FEM.
So as an ice breaking for the forum, I have made a dialogue between me and an imaginary student who asks about differential equation. I share herein the dialogue for your reading. Please enjoy.
Student: What is a differential equation?
Dr Airil: Differential equation or DE is a mathematical statement that contains the relevant information about the physical problem at hand.
Student: Since it is contained, how can we get this information?
Dr Airil: We can get the information by solving the DE.
Student: How do we know that this information is correct?
Dr Airil: The information is correct if the DE is correct and if we solve the DE correctly.
Student: When a DE is correct and when it is wrong?
Dr Airil: A DE is correct if it is derived by satisfying the conservation laws of mass, energy and momentum. It is wrong when the derivation violates these laws.
Student: How can we solve a differential equation?
Dr Airil: We can solve DE in many ways but not all will work. We can solve analytically by direct integration, undetermined coefficient method etc. or semi analytically by Laplace Transform, Fourier Transform etc. or numerically by finite difference method, boundary element method and of course finite element method.
Student: Let's say that we have derived a new DE? How can we know whether it is right or wrong?
Dr Airil: Ok, let's say that we have derived a new DE, we then must solve it. The solution or the information that we just obtained by solving the DE remains as a hypothesis until we verify it. If verified, then we know that our DE is correct and we can claim to have our own new theory. Huh, how cool is that?
Student: But, how can we verify the solution?
Dr Airil: Basically, there are two major ways of verification of DE and its solution. One is by verifying it with experimental tests or physically measured data and two, by verifying it with an established solution of another DE which we can argue to certain extent the equivalency and representativeness between the two.
Student: Why DE is difficult to learn?
Dr Airil: It seems to be difficult because one, you are not told of the importance of DE and two, you are not told of the 'story' of DE. If you know these two (I hope by now you know at least a bit from our discussion), you will see how DE is actually very easy.
Student: You said that learning of DE can be easy if we know the importance. What is the importance of DE?
Dr Airil: As I said, DE contains information. These information if exploited can make all the changes in the world. You can build the fastest car, you can send people beyond mars, you can make new medicine, and you can do all the good things. Actually, understanding and exploiting DE are what differentiate us from the advanced countries. Wallahualam.
Student: Thanks
Dr Airil: Don't mention it, my pleasure
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