Help with my Project!

Surely, as a forth-year ME student, you have run across "differential equations" before, not to mention "typical engineering problems!"

If not, you ain't getting much of an education!

If you really want advice, give us some indication of your experience with each of the things in quotes above.

Sorry, I ment that my college needs 4 years to get a degree.i am at 2nd senester.

Well, where do I start?

There are "ordinary" and "partial" differential equations with which you will eventually deal, but the good part is that they're similar, mathematically speaking. In engineering departments, they may be called "eigenvectors," or something like that, but don't let that scare you. Sometimes, coefficients of differential equations may be put in a matrix or determinant to enable a mathematical solution, so you'll need to know about matrices and determinants too.

Bottom line? Four semesters or more of math! It's spread out over a few years for a reason: There's a lot to learn. Pay attention to uses of differential equations in solving engineering problems. If you can "shop" for professors who have knowledge of uses of mathematics in engineering and physics, try to get in their classes.

One of the few times in my life that I used partial differential equations was to determine the cause of temperature fluctuations in a high temperature oven that we were trying to maintain at 500^oC within a half of a degree (we were getting close at +/- 1^oC). After mathematically modeling the thermodynamic process and applying a little error analysis through the use of partial differential equations, it became obvious that the physical mass of the oven was too low, and that we needed to add thermal mass in the form of a steel plate (which is similar to increasing the mass of a flywheel to minimize fluctuations in angular velocity with a given power input).

This is but the tip of the iceberg, so to speak. There are thousands of engineering problems all over the world which will be solved over and over again, because one problem may be similar to another, but it isn't exactly the same, so there's no catalog of solved problems (except for the classical textbook problems, and they're for teaching you the techniques of solving problems).

To figure out for yourself what kinds of engineering problems you may face (regardless of the tools (e.g. math) you use to solve them), ponder what problems you would face if you started to design the space shuttle, a water dam, a skyscraper, an automobile, a robot to explore the depths of the ocean or the surface of Venus, etc.

My personal advice? Take your time and learn well. Too many engineering students didn't pay enough attention to connections between mathematics and the real world, and unfortunately, some professors never "got it" either.

I have a question, a simple one:

Sometimes, coefficients of differential equations may be put in a matrix or determinant to enable a mathematical solution, so you'll need to know about matrices and determinants too.

In general matrix are used to solve algebraical LINEAR equation systems. Of course this part of mathematics is very useful and one has to master them but my limited knowledge does not show me where this can be used for the solving of differential equations if we of course not consider the finite element approach based totally on matrix products. When we reach this part of solving then the solution is to use solvers since those systems are huge (many elements lead to even more knots and balance equations) and no user will build his own solvers.

And any way the matrix is not build up with the coefficients but with the knots parameters.

In many cases, systems are defined by several differential equations, and one of the methods used is to put them in matrix or determinant forms to solve for values. It's the same technique one would use for a system of linear equations.

If you check out an advanced book on Linear Algebra, you should find the technique of which I speak.

Finite Element Method came along (grew in popularity) when computing reached the point that it could be used efficiently. Prior to that, it was only used by masochists!

Linear algebra makes use of matrix but for differential equations it is a bit different.

Which do you hate more, not being right, or allowing anyone to know more than you?

As you said, " . . . my limited knowledge does not show me where this can be used for the solving of differential equations . . ."

Like I said, " . . . check out an advanced book on Linear Algebra . . ."

Oh I do not know what You hate more but your reaction is quite interesting!

Please since you are SOOOO clever and know SOOOOO much give me some examples so that I can learn from your Highness.

Thank you in advance for what you will teach me.

You have quite an ability to express sarcasm in print! I didn't start this process of one-up-man-ship, but I got the distinct feeling that you didn't believe what I wrote and decided to attack me for it.

I'll have to get back to you with an example, primarily because I don't know how to get the mathematical symbols into this dialog box.

On the other hand, you have nearly answered your own question in your subsequent post by suggesting that he would need to know about LaPlace transforms which is a tool to convert differential equations to algebraic ones. Algebraic equations can be solved by the use of determinants. Do you agree?

I shall try to give some explanations since what you got is at a too high level to be understood by a normal human being.

As a ME you will have to deal with several types of problems which can be parted in 2 main categories:

- concentrated parameters

As an example a mass/spring/damper system where the spring mass is small with respect to the main one.

- bulk problems

In the 1st category you can find most of mechanical systems when you analyse their dynamic behaviour or for instance the heat conduction along a bar where due to the small transverse dimensions the temperature can be considered as constant over the section so that the temperature field depends only on the axial coordinate.

The second category considers problems where a 3 dimensional analysis is required. Such problems are for instance the strain distribution in in a body, heat conduction, flow dynamics, aso. Some times for different reasons the problems can be simplified (as shown above) and a simpler analysis can be done. For the second category the most precise approach is the use of partial differential equations or systems as the Fourier one for heat or the Navier-Stokes for fluids. Those are partial differential equation of the second order.Even in systems as a bar the axial transmission of a wave has to make use of a partial differential equation due to the distributed mass and stiffnesses. If the precision required is not too high then it is possible to use in place of the continuum a series of mass-spring systems and build up a system of linear equations of course a lot easier to solve.

As you see there is no preferential domain or equation- unfortunately- you have to make the effort to learn all of them.

If we come to the 1st category back, there is an approach which allows a much simpler way to obtain the solution provided that the equation is linear ( i.e. all derivatives of the function are at power 1) or it allows a linearizing around a working point.

This approach is called the Laplace Transform which allows the transformation of a linear differential equation in an algebraic one. Such equations or systems are easy to handle with the usual tools for algebraic systems. There are tables for the conversion of the obtained solution in the transform domain to the original domain.

To lessen your fears, to day there are a lot of programmes for solving equations or systems. The most important for an engineer is the understanding of the physical process and based on that to be able to write the correct equation/system and also to estimate what can be neglected and what MUST be maintained.

A last explanation, the question is when and where will be you confronted to differential equations? Mostly this occurs when you have to make a simulation and with its help an optimisation of a process, of a part or anything else.

I apologize for the reaction of King William the 1st of Difeq but as you will notice later in you professional life many people are so proud of the few they know that they do not accept a contradiction.

And for the comment about finite elements analysis, before the computer was made available almost to every body by the PC or Mac the method was already developed and used with bigger elements, with less accuracy but with many positive results.

I shall take the opportunity to answer the question :

- the most I hate is arrogant stupidity.