Some Suggestions for Problem Solving- Prof. M. Kostic

Some Suggestions for Problem Solving: *
[Example] *** Your feed-back/comments are welcomed!

Until recently I was convinced that students have first to understand the problem before they start solving it. That is how we, teachers (experts) solve characteristic (simple) problems, but it is virtually impossible for the novice students. Furthermore, if you understand a problem it is no longer the problem. Actually one will understand the problem after solving it, not before. What is needed is to understand "what the problem ask for and how it relates to our relevant knowledge and experience" in order to start solving it, and then previous step will lead to the next one, until we solve the problem (using our intuition, creativity, trial-and-error attempts, and what-if analysis and syntheses). In other words, start a problem solution by responding to what the problem asks for. Then, each step is a consequence of the previous step and a predecessor to the next step (easier said than done!). Actually, the problems tend to solve themselves!

NOTE: Engineering, real-life problems are not as exact as math ones. Sometimes, the solution may be based on approximations and assumptions, and sometimes that is the only way to start solving a problem, and only after the result is obtained the original assumptions may be improved/corrected if they depend on the final result. That is a common and often way of solving a real-life problems by trial-and-error or iteration. What is really important is to take a good look at the calculated result (do not forget units) and try to evaluate and justify its validity: is it physically possible, reasonable, and what assumptions and approximations, if any, it is based on. That will often help you remove a “silly” mistake(s) or correct/improve the solution. Your comments, if appropriate, will show that you are aware of (understand) your work and reality. Hope this will be of help.

OBJECTIVES ARE:
NOT just to substitute values into formulas and calculate results - computer software do it for us, but
TO understand, formulate and solve problems, and
TO evaluate, justify and interpret results.

(the most common steps, some may not apply to your problem or additional steps may be needed)

Read and understand physics of the problem. It should make sense, if not, read it again.

Choose/define and sketch the system of interest, and find appropriate interactions across its boundaries.

Determine the process(es) and influential variables and properties (knowns and unknowns, inputs and outputs, etc.).

Organize the knowns and unknowns in a logical table if appropriate and fill in known data.

Determine "workings" of the process and sketch its diagram or other diagrams. One picture is worth a thousand words, I think even more.

Apply relevant "governing" equations (e.g., balance of forces; conservation of mass, momentum, and energy principles; rate equations, property relations, etc.).

Bring in other information, physical constrains, boundary conditions, etc.

Develop enough equations for the unknowns and SOLVE the problem.

If stuck, review the work done, and readjust/modify your approach and work if needed.

Check the variables' dimensions and that the results are logical, physically possible and meaningful.

[Example] * [Tips for Learning and Academic Skills Improvment]