Recent content by Unstable

I know that this is the opinion of many people but it is definately NOT TRUE! Don't get me wrong, I just want to say that in DE related subjects in universities not enough focus is given to application which is a tremendous disadvantage expecially for mathematicans.

Thanks so far the answers. I do not totally disagree with the presented arguments but I still have the opinion that this important field in mathematics, which has so much great potential in application, is educated in a wrong way at Universities. I am a mathematician who learned the...

After a short look on the question formulated in this differential equation forum I came to the conclusion that the teaching of DEs at Universities goes in a wrong direction. The aim of DEs is not “how could I solve them” the point is “what I could do with them”. In practice nobody solves DEs...

EDIT: DEs are the perfect example where theoretical math fails (for students and most users, don't get me wrong theoretical stuff is important but should not be only thing) The question is not why my car is red and has 4 wheels (and not 7 maybe), the question is why I could drive from A to B...

Wow… that is different to my course… I learned only theoretical stuff! Nevertheless, I want to say that I am an expert in ODE modeling with biological background and we have to go back to the basics. The traditional ideas of DES are what?

That’s it! People, especially pure math orientated have to understand that Des (ODE, PDE, DDE,…) are more than just objects to study from a mathematical point of view. Unfortunately, until now most math courses about Des are about theoretical properties. No doubt, this is important, but these...

You should ask yourself what is your interest on PDEs? Theoretical properties, numerical issues, modeling of e.g. biological phenomena, … ? What was your interest when studying ODEs?

Einstein… okay I am not sure what you mean. This guy made definitely some non-linear stuff. From your initial post I sought you have some problems to determine if an ordinary differential equation is linear or non-linear. Before you start with some fancy DEs you have to understand what a DE...

Think on what you learned at school. A linear function (really a straight line) is of the form y= a\cdot x + b Now a differential equation of the form x'(t) = A(t) \cdot x(t) + b(t) \qquad \qquad (*) is a linear differential equation. (Note the dependency on t) Again back to school, a...

I would recommend to google for "linear differential equations" and look for similar examples. The net is full with scripts about this topic. Without knowledge in DEs it is nearly impossible to find the solution in this case. Alternatively, also the Laplace transfom (which I actually...

You can also easily write the solution with the help of the matrix exponential. But I guess that is not what you want. I always wonder when people start to apply differential equations as model for some situations, do they really understand why the differential equation describes the stated...

Do you want to implement RKF? Why? Use ode45 in Matlab, which is RKF. There you have step size control and everything. (RK with fixed step size is just for academic considerations suitable. In practice, fixed step sizes are horror.) Additionally, if you have problems with an explicit solver like...

My observations about „higher“ math in PhD projects and research are that the topics strongly changed from the typical pure math to more applied math in the last years. At least in Germany, Universities force their departments to collect money from industry. That means you have to do something...

First, it is much easier for beginners to consider the dependencies of t in the functions. So in your example x is x(t). Try to write the differential equations in the following form: x’(t) = A(t)x(t) + g(t) If this is possible it is a linear differential equation. In your first...

Wow...