If we had a large number of such problems to solve, generalized the above example to read as follows John's age in 3 years Mary's age in 3 years Mary is now four years older than John, and be twice his age. Them "word problems" or "story problems." You will remember that they are often more difficult than routine manipulations, but success in solving these kinds of problems is of the utmost importance Let us consider a very famiUar example of such a to a scientist. In algebra you have already met problems of this tvpe and have called In most such situations, you will need to rely upon your mathematics, and frequently you will have to do some real thinking. statements and asked to draw a conclusion from You will often be confronted Analysis of Scientific Situations. Since you will, therefore, have to know mathematics in order to understand what your science teachers are saying, mathematics may well be thought of as the "language of science." If you do not understand the language, you cannot learn science. After the terms of science are defined, statements about them must be made and these generally appear as mathematical equations. Indeed, these basic concepts of physics cannot be defined until we have reached the final chapters of this book. ity" and "acceleration" remain vague until the}' are expressed in mathematical terms. Although 3'ou doubtless have an intuitive idea of the meaning of "the area of a circle," we cannot define this precisely without the In the same way such familiar notions as "velocuse of the calculus. Since much of science is based on measurement and is therefore quantitative in character, these technical definitions are best expressed in terms of mathematics. This is especially important in science where words are used with very precise meanings. To learn the meanings of the special, technical The real reasons why a scientist must know great ease When you do so, however, you must remember that you are acting as a machine and not as a human being. Since these machines are expensive and are not particularly efficient vrhen used on simple problems, you must still learn to calculate. expression which relates one letter to a specific values of these last lettersīy modern high-speed calculating machines. To do so, you must learn the rules and develop speed and accuracy in your calculaAll of this, however, is basically mechanical and requires no tions. For you are asked to determine the value of the first letter by following a prescribed set of rules. At the very beginning you will meet other types of functions such as the trigonometric, logarithmic, and exponential functions and before you You have probably met formulas which are more complicated algebraic expressions, but even these do not cover all the needs of science. Only the simplest processes of algebraīut not all the formulas of science are so elementary. (a)įor a specific value of r (say 2 in.) you now calculate A, and for a given time interval (say 3 sec) you calculate s. Let us, then, consider various ways in which mathematics is used by practicing scientists. As a potential scientist you are studying this book to learn some of the mathematics that you will need in your own field, but before you can appreciate the mathematics to come you need to know something of the nature of mathematics and its relationship to science. The basic ideas and relationships in the physical sciences have been expressed in mathematical terms for a very long time, and in recent years the use of mathematics in the biological and social sciences has increased tremendously. science or engineering, you were undoubtedly told that you would have to learn a good deal of mathematics in order to be successful in your career. When you became interested in the study of. Second Derivative The Chain Rule Maxima and Minima Related Rates Mid-point of a Line Segment Directed Line Segmentĭirected Lines Plane Geometry The Straight Line Conic Sections Case I.
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