Techniques of Problem Solving

Your objectives in studying this section are to be able to  

Memorize the eight components of effective problem solving. 

Weiler s Law Nothing is impossible for the person who doesn t have to do it. 

Howe s Law Every person has a scheme which will not work. 

Gordon s Law If a project is not worth doing, it s not worth doing well. 

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In this chapter we have introduced symbolic mathematics, which involves the manipulation of symbols instead of performing numerical operations. We have presented the algebraic tools needed to manipulate expressions containing real scalar variables, real vector variables, and complex scalar variables. We have also introduced ordinary and hyperbolic trigonometric functions, exponentials, and logarithms. A brief introduction to the techniques of problem solving was included. 

If problems baffle you, learn the technique of problem solving. The principles contained in G. Polya s book, How to Solve It, have helped many of my students. It is available as a paperback and is well worth studying. Work as many problems as possible. Numerical answers to all problems can be found in Appendix VII. Make up your own problems as often as possible. Watching your teacher perform will not make you into an actor problem solving will. To aid in this, get a good scientific calculator (the serious student will want a programmable one with continuous memory) and learn how to use it to the limit of its capability. Reading the instructions will save you hundreds of hours ... 

Techniques of problem solving are applicable to many intellectual areas. There is a useful little book on problem solving by Polya, and much of our discussion of problem solving is based on this book. Most physical chemistry problems are stated verbally, like the so-called word problems of elementary school. The information contained in the statement of the problem generally includes a statement of the physical system involved, some information about the state of the system, and a statement of the desired outcome. In many problems, the desired outcome is a numerical value of some variable that can be calculated. Following is arecipe for approaching such a problem ... 

A severe limitation of the effective use of ozone in organic synthesis is its low solubility in organic solvents. The so-called dry ozonation technique of Mazur solves this problem.102 Dry silica gel with the preadsorbed organic substrate is saturated with ozone at —78°C. After warming up to room temperature, the products are eluted in the usual way. Under these conditions ozone exhibits an enhanced reactivity presumably due to the slightly acidic nature of silica gel 103... 

Many comprehensive texts have been written on the theory and practice of fluorine-19 NMR spectroscopy12-14, so to reproduce such detail here is unnecessary. In this section only the basic principles will be discussed followed by a description of how fluorine-19 NMR has been used in a number of problem-solving activities. Such an approach will not be completely comprehensive and will reflect the interests of the authors. However, it is hoped that the power of the technique will be conveyed to the reader. Many studies have been performed on the theory of fluorine-19 NMR, however, it does not seem appropriate to present them in detail in this chapter. 

There are a variety of problem-solving strategies that you will use as you prepare for and take the AP test. Dimensional analysis, sometimes known as the factor label method, is one of the most important of the techniques for you to master. Dimensional analysis is a problem-solving technique that relies on the use of conversion factors to change measurements from one unit to another. It is a very powerful technique but requires careful attention during setup. The conversion factors that are used are equalities between one unit and an equivalent amount of some other unit. In financial terms, we can say that 100 pennies is equal to 1 dollar. While the units of measure are different (pennies and dollars) and the numbers are different (100 and 1), each represents the same amount of money. Therefore, the two are equal. Let s use an example that is more aligned with science. We also know that 100 centimeters are equal to 1 meter. If we express this as an equation, we would write ... 

One of the usual responsibilities of an engineer is problem solving, e.g., process troubleshooting. Using an established technique of problem analysis, you can become a better problem solver by knowing which problem to attack first. The Pareto chart is one of the most powerful tools in problem solving, yet is often overlooked in U.S, industry. 

Hyphenated techniques refer to the combination of one or more analytical techniques for problem solving and fundamental research. Numerous types have been reported in the scientific journals. Frequently the FTIR spectrometer is coupled with chromatographic instruments for the structural characterization of a column eluent. These systems are designed to monitor the eluent or to obtain its spectrum. Much of the development has been focused on the sampling technique and the design of the interface between the chromatographic system and the FTIR spectrometer to improve the performance of the system. 

ICP-OES continues to dominate the market because of its ease of use and relatively low maintenance cost. Inductively coupled plasma mass spectrometry (ICP-MS) is a very powerful state-of-the-art technique used for metal analysis of all kinds of samples but requires highly skilled operators. A vast amount of information is received that is not necessarily required as part of problem-solving or routine support. The cost difference and relative freedom from maintenance problems would favour ICP-OES. This book is aimed at practitioners requiring multi-elemental analysis in industrial, environmental, pharmaceutical and research laboratories, where information on identification and quantification is required on a regular basis. The main focus of this book will be on sample preparation, a topic overlooked in most books on atomic spectroscopy. It is aimed at most ICP-OES and ICP-MS users to show that the instrument is useless unless the sample is prepared in a suitable state that can be used to accurately and precisely quantify the metals present. 

The methods and techniques of expertise studies have direct value for schema research. Much of what we want to study shows up in intermediate, rather than final, stages of problem solving, and we need procedures that will allow us to gather a wide variety of data. The techniques of Figure 6.1 can be easily adapted for schema study, as will be seen in subsequent chapters. 

There are a variety of problem-solving strategies that you will use as you prepare for and take the AP exam. Dimensional analysis, sometimes known as the factor label method, is one of the most important of the techniques for you to master. 

Regardless of the analytical instrumentation mix, the art of problem-solving remains. A person or team must make the decisions about analysis what, when, and how. There must be an analytical "ejqpert" be it man or computer, who can make choices of appropriate technique. 

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