CHAPTER 1MATHEMATICS AND UNITSOF MEASUREMENTMathematics is the Engineering Aid’s basictool. The use of mathematics is found in everyrating in the Navy, from the simple arithmeticof counting for inventory purposes to thecomplicated equations encountered in computerand engineering designs. In the Occupational Field13 ratings, the Engineering Aid is looked uponas superior in knowledge when it comes to thesubject of mathematics, which generally is acorrect assumption; however, to be worthy of thiscalling, you have the responsibility to learn moreabout this subject. Mathematics is a broad sciencethat cannot be covered fully in formal serviceschool training, so it is up to you to devotesome of your own time to the study of thissubject.The EA must have the ability to computeeasily, quickly, systematically, and accurately.This requires a knowledge of the fundamentalproperties of numbers and the ability to estimatethe accuracy of computations based on fieldmeasurements or collected field data. To computerapidly, you need constant practice and shouldbe able to use any available device to speedup and simplify computations. In solving amathematical problem, you should take adifferent approach than you would if it weresimply a puzzle you were solving for fun.Guesswork has no place in its consideration, andthe statement of the problem itself should bedevoid of anything that might obscure its truemeaning. Mathematics is not a course in memorybut one in reasoning. Mathematical problemsshould be read and so carefully analyzed that allconditions are well fixed in mind. Avoid allunnecessary work and shorten the solutionwherever possible. Always apply some proof orcheck to your work. Accuracy is of the greatestimportance; a wrong answer is valueless.This chapter covers various principles ofmathematics. The instructions given will aid theEA in making mathematical computations in thefield and the office. This chapter also covers unitsof measurement and the conversion from onesystem to the other; that is, from the English tothe metric system.FUNDAMENTALS OFMATHEMATICSMATHEMATICS is, by broad definition, thescience that deals with the relationships betweenquantities and operations and with methods bywhich these relationships can be applied todetermine unknown quantities from given ormeasured data. The fundamentals of mathematicsremain the same, no matter to what field they areapplied. Various authors have attempted toclassify mathematics according to its use. It hasbeen subdivided into a number of major branches.Those with which you will be principallyconcerned are arithmetic, algebra, geometry, andtrigonometry.ARITHMETIC is the art of computation bythe use of positive real numbers. Starting with thereview of arithmetic, you will, by diligent effort,build up to a study of algebra.ALGEBRA is the branch of mathematics thatdeals with the relations and properties of numbersby means of letters, signs of operation, and othersymbols. Algebra includes solution of equations,polynomials, verbal problems, graphs, and so on.GEOMETRY is the branch of mathematicsthat investigates the relations, properties, andmeasurement of solids, surfaces, lines, and angles;it also deals with the theory of space and of figuresin space.TRIGONOMETRY is the branch of mathe-matics that deals with certain constant relation-ships that exist in triangles and with methods bywhich they are applied to compute unknownvalues from known values.STUDY GUIDESMathematics is anmany books on theexact science, and there aresubject. These numerousl-l
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