Mechanical Engineering Problems and Solutions, 6th Edition
With this guide, you'll hone your problem-solving skills as well as your understanding of both fundamental and more difficult topics for the Professional Engineering exam.
TABLE OF CONTENTS Mechanical Engineering Problems and Solutions, 6th Edition
Chapter 1: Mathematical Fundamentals
Peter A. Szego
A survey of the entirety of applied mathematics is beyond the scope of this review. Instead we focus attention on a number of common stumbling blocks. Although all of these are of an elementary character, experience has shown that they are at the root of a high proportion of errors in engineering mathematics.
FORMULA SUBSTITUTION
As simple a matter as substituting in formulas sometimes causes difficulties. Consider for example the quadratic equation, along with its solution, as expressed by the formulas:
A numerical example, say 2x 2 ? 3x + 5 = 0, is handled in a straight forward manner. We either make the substitutions mentally or (to be quite certain) we make up a little equivalence table, thus:
Sometimes, however, we must deal with a quadratic equation written as a formula (i.e., with symbol coefficients) and, moreover, some of the symbols may coincide with those in the "standard" form. For example, suppose we wish to solve for z in 2z 2 + az + c = 0. To avoid confusion we need to distinguish the "a" and "c" of our problem from the like symbols in our reference formula. One way to do this is to use some special mark on the symbols of the reference formula, thus:
Once more, we set up an equivalence table:
so that
The discussion of the quadratic equation is only by way of example. The problem of symbol substitution arises in all areas of mathematics. Texts and reference...
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