Using Science to Solve Problems

Constraints in optimization arise because a process must describe the physical bounds on the variables, empirical relations, and physical laws that apply to a specific problem, as mentioned in Section 1.4. How to develop models that take into account these constraints is the main focus of this chapter. Mathematical models are employed in all areas of science, engineering, and business to solve problems, design equipment, interpret data, and communicate information. Eykhoff (1974) defined a mathematical model as a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in a usable form. For the purpose of optimization, we shall be concerned with developing quantitative expressions that will enable us to use mathematics and computer calculations to extract useful information. To optimize a process models may need to be developed for the objective function/, equality constraints g, and inequality constraints h. 

Noble Gas Geochemistry discusses the fundamental concepts of using noble gases to solve problems in the earth and planetary sciences. 

Technology is the use of scientific knowledge to solve problems. For example, science studies the flow of electrons but technology takes the flow of electrons to create a supercomputer. Mathematics, in turn provides the language to allow this knowledge to be communicated. It creates models for science to use to explain natural phenomena. 

This book is designed to help you leam the fundamentals of chemistry. To be successful, you must master the concepts of chemistry and acquire the mathematical skills necessary to solve problems in this quantitative science. If your algebra is rusty, you should polish it up. Appendix 1 reviews the algebra used in basic chemistry and also shows how to avoid mistakes while solving chemistry problems with your scientific calculator. The factor label method is introduced in Chapter 2 to show you how to use units to help with problem solutions. You can help yourself by using the standard symbols and abbreviations for various quantities (such as m for mass, m for meter, mol for moles, and M for molarity). Always use the proper units with your numerical answers it makes a big difference whether your roommate s pet is 6 inches long or 6 feet long ... 

In the early stages of its development, MAS NMR tended to be the preserve of specialist spectroscopists and theoreticians, but, as its possibilities have become better known, it has become very much a technique used by engineers and scientists to solve real problems. The literature, which was once found mainly in fundamental and highly technical texts, is now just as likely to be found in applied science journals, as increasing numbers of non-specialist researchers turn to MAS NMR to solve problems in real and often non-ideal systems. 

The ability of chemists and other physical scientists to more effectively collaborate with biological scientists and medical doctors is essential for the future of mankind. Nearly all problems facing us in this area require multidisciplinary approaches and ideas. The ability to effectively communicate and collaborate to solve problems in disease and diagnosis with mutual respect and without any arrogance of any field or discipline is critically required. The very serious ethical and social issues that modem science raises requires cQl scientists and medical practitioners to take seriously their own responsibility for what they invent and how it will be used in society. 

Effective use-research and technical service depend, fundamentally, upon the experimental sciences as practiced by chemists and engineers in modem laboratory settings. Within reasonable limits, the capacity of these functions to consider and to solve problems of concern to customers does not relate to the total number of members assigned to these functions nor to the dollar level of the budget. In this setting, the motivation of the individual experimentalist and the leadership skills of his manager count heavily in the productivity. 

Different configurations allow different methods to be examined to solve problems. This is useful in developing tests and research science... 

In the last section we began to see how the methods of science are used to solve problems. In this section we will further examine this approach. 

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