Step 1: Defining the Problem
Before you can obtain an appropriate solution to a problem, you must first thoroughly under-
stand the problem itself. There are many questions that you need to ask before proceeding to
determining a solution. What is it exactly that you want to analyze? What do you reallyknow
about the problem, or what are some of the thingsknownabout the problem? What are you
looking for? What exactly are you trying to find a solution to?
Taking time to understand the problem completely at the beginning will save lots of time later
and help to avoid a great deal of frustration. Once you understand the problem, you should be able
to divide any given problem into two basic questions: What is known? and What is to be found?Step 2: Simplifying the Problem
Before you can proceed with the analysis of the problem, you may first need to simplify it.
Assumptions and Estimations Once you have a good understanding of the problem, you should
then ask yourself this question: Can I simplify the problem by making some reasonable and log-
ical assumptions and yet obtain an appropriate solution? Understanding the physical laws and
the fundamental concepts, as well as where and when to apply them and their limitations, will
benefit you greatly in making assumptions and solving the problem. It is very important as you
take different engineering classes in the next few years that you develop a good grasp of the
fundamental concepts in each class that you take.Step 3: Performing the Solution or Analysis
Once you have carefully studied the problem, you can proceed with obtaining an appropriate
solution. You will begin by applying the physical laws and fundamental concepts that govern
the behavior of engineering systems to solve the problem. Among the engineering tools in your
toolbox you will find mathematical tools. It is always a good practice to set up the problem in
symbolic or parametricform, that is, in terms of the variables involved. You should wait until
the very end to substitute for the given values. This approach will allow you to change the value
of a given variable and see its influence on the final result. The difference between numerical
and symbolic solutions is explained in more detail in Section 6.5.Step 4: Verifying the Results
The final step of any engineering analysis should be the verification of results. Various sources of
error can contribute to wrong results. Misunderstanding a given problem, making incorrect
assumptions to simplify the problem, applying a physical law that does not truly fit the given prob-
lem, and incorporating inappropriate physical properties are common sources of error. Before you
present your solution or the results to your instructor or, later in your career, to your manager, you
need to learn to think about the calculated results. You need to ask yourself the following question:
Do the results make sense? A good engineer must always find ways to check results. Ask yourself
this additional question: What if I change one of the given parameters. How would that change
the result? Then consider if the outcome seems reasonable. If you formulate the problem such that
the final result is left in parametric (symbolic) form, then you can experiment by substituting dif-
ferent values for various parameters and look at the final result. In some engineering work, actual
physical experiments must be carried out to verify one’s findings. Starting today, get into the habit4.2 Basic Steps Involved in the Solution of Engineering Problems 93
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