How to Solve It

The shaded terms cancel out. Multiplying by the factor (1 —1/2 ) has evidently removed all the terms divisible by 2 from the zeta-function series. The next step is to multiply by (1 — 1/3 ). This gives 

Continuing the process, we successively remove all remaining terms containing multiples of 5, 7,11, etc. Finally, we obtain 

Although we had promised not to give you any mathematical good advice in abstract terms, the book by Georg Polya, How to Solve It (Princeton University Press, 1973), contains a procedural approach to problem solving, which can be 

You have to understand the problem. What is the unknown What are the data What is the condition Is it possible to satisfy the condition Is the condition sufficient to determine the unknown Or is it insufficient Or redundant Or contradictory Draw a figure. Introduce suitable notation. Separate the various parts of the condition. Can you write them down  

Carry out your plam Carrying out your plan of the solution, check each step. Can you see clearly that the step is correct Can you prove that it is correct  

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Chittenden, D. H. (1987) Chem. Eng., NY94 (March 16) 89. How to solve it revisited Engineering problem solving approach. 

Characteristics and Values of Expert Systems. What leads me to make such bold and risky statements The answer can be summarized as follows. First, knowledge is power. You can t solve problems using any technology unless you have some detailed knowledge about the problem and how to solve it. This fact seems so obvious that it is unnecessary to state it. Many systems will fail, however, because the builders will attempt to build such systems to solve ill-defined problems. 

Polya, G. (1973), How To Solve It A New Aspect of Mathematical Method, 2nd ed., Princeton University Press, Princeton, NJ. 

T. E. Bearden, The unnecessary energy crisis How to solve it quickly, paper presented to Association of Distinguished American Scientists (ADAS), June 24, 2000 (an ADAS position paper on the subject). Also on http //www.cheniere.org. 

There is no doubt about the importance of n, the principal quantum number, but where does it come from This quantum number and two other quantum numbers come from solving the Schrodinger equation. We are not going to go into any details regarding Schrodinger s equation or how to solve it—there are plenty of more specialized texts available if you are interested in more detail. 

Michalewicz Z, Fogel DB (2000) How to solve it modern heuristics. Springer, Berlin Heidelberg New York... 

Figure 1.14 Program for problem solving. G. Polya, How to Solve It, 2nd ed., Doubleday, New York, 1957.

R. G. Dromey, How to Solve It by Computer. Prentice-Hall International, Englewood Cliffs, NJ, 1982. 

G. Polya, How to Solve It, A New Aspect of Mathematical Method, 2nd ed., Princeton Univ. Press, Princeton, NJ, 1957. This small book is out of print but it should be in every college or university library. It contains a detailed discussion of general methods of solving problems. 

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 ... 

Didn t mention formulas or equations until they had said how to solve it in chemical terms. 

Polya, G. (1946). How to solve it a New Aspect of mathematical method. Princeton, NJ Princeton University Press. 

In the following sections we show how to construct a suitable model of the process and how to solve it for a given case. We win show only deterministic models of convective drying. Models beyond this range are important but relatively less frequent in practice. 

HICKS Yes, it s definitely a dynamic transfer process. I think the picture we ve had in the back of our minds for a number of years is one of transfer to pipes, flat plates, and smooth surfaces. I don t think that s really appropriate when we re talking about a surface like a forest. One might ask whether we should wash the Inside of the collecting buckets and the outside, too It s a difficult situation and I don t really know how to solve it. 

Solving a problem with one finger at its solution in the answer section so you can check your progress is neither solving the problem nor learning how to solve it. When you tackle a problem, solve it completely. If you get stuck at any point, put the problem aside and check the part of the chapter that covers that point. Learn there what you need to learn. Do not check the answer section. Return to your solution of the problem and complete it. Then compare your solution to the one in the back of the book. If they do not agree, find out why. Be sure you understand the problem before going to the next one. 

Believe it or not, this is an easy problem Don t let the words and unfamiliar terms bother you. By reading the problem, you should be able to decide how to solve it. Once you know that, it is routine. Plan your approach by writing the Given quantities and the Wanted units, and state your decision. 

However, blank space between the two values may mean an addition or a multiplication. For example, 2 h, 30 min, 1 km, 200 m etc. Here the invisible addition sign stands between the same quantities (time and length), and multiplication sign - between the constants and the units. Figure 6.53 shows how to solve it in Mathcad. 

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