Problem-solving, analytical approach

Having noted that each field of chemistry brings a unique perspective to the study of chemistry, we now ask a second deceptively simple question. What is the analytical perspective Many analytical chemists describe this perspective as an analytical approach to solving problems. Although there are probably as many descriptions of the analytical approach as there are analytical chemists, it is convenient for our purposes to treat it as a five-step process ... 

Read a recent article from the column Analytical Approach, published in Analytical Chemistry, or an article assigned by your instructor, and write an essay summarizing the nature of the problem and how it was solved. As a guide, refer back to Figure 1.3 for one model of the analytical approach. 

Subsection of the analytical approach to problem solving (see Eigure 1.3), of relevance to the selection of a method and the design of an analytical procedure. 

Simulations. In addition to analytical approaches to describe ion—soHd interactions two different types of computer simulations are used Monte Cado (MC) and molecular dynamics (MD). The Monte Cado method rehes on a binary coUision model and molecular dynamics solves the many-body problem of Newtonian mechanics for many interacting particles. As the name Monte Cado suggests, the results require averaging over many simulated particle trajectories. A review of the computer simulation of ion—soUd interactions has been provided (43). 

The power of TLC is in its flexibility as a problem solving tool. As the problems in analysis become more complicated the sophistication by which we approach those problems is ever increasing. However, it behooves us as analytical chemists not to forget our fundamental training in chemistry and to apply those principles to today s problems. It is just this feature that the reader will find instilled into this book. 

Several analytical methods are available to quantify chlorophylls and choice depends on the information needed. For quality control in industries and legislation attendance, simple and cost-effective methods represent widely used problem-solving approaches. For research purposes, more sensitive and precise methods are necessary to identify chlorophylls and derivatives simultaneously and individually. 

Meglen RR (1990J Analytical problem solving, reference materials, and multivariate quality control A chemometrics approach. Fresenius J Anal Chem 338 363-367. 

Define the analytical approach, such as the material and the analytes to be looked for so as to (possibly) answer the questions asked and to solve the problems. Select an appropriate analytical method, with definition of its purpose and utility. If none of the available methods fits the analytical purpose, try to deduce method approach(es) from existing methods for structurally related compounds or materials by introducing carefully selected modifications and adaptations. 

Polymer/additive analysis is a typical industrial analytical problem, and indeed not one of the easiest or least important ones. Requirements set to industrial analytical expertise vary from new analytical approaches for product innovation, to service-oriented problem solving (combination of analytical expertise and specific product knowledge), and cost-efficient analysis of a few grades (plant service) (Scheme 10.1). Reported prospects set the instrumental trends in the polymer industry (Table 10.17). For traditional quality laboratories this translates into ... 

Example 3.2 Solve the problem in Example 3.1 using an analytical approach. 

In many problems for which no direct solution can be obtained, there is a wave equation which differs but slightly from one that can be solved analytically. As an example, consider die hydrogen atom, a problem that was resolved in Section 6.6. Suppose now that an electric field is applied to the atom. The energy levels of the atom are affected by the field, an example of the Stark effect. If die field (due to the potential difference between two electrodes, for example) is gradually reduced, the system approaches that of the unperturbed hydrogen atom. 

Due to a lack of understanding in the use of analytical skills, most people resort to disconnected problem solving techniques to analyze their problems in lieu of a structured logical approach. This stems from the fact that we do not give analysts the tools necessary to do their jobs. Simply put, many of today s analysts lack the proper mentoring and training necessary to accomplish the desired result—the elimination of problems. Without these tools these analysts revert to their inherent god-given analytical techniques i.e., inference, perceptions, assumptions, intuition and reports by others. 

In many cases the equality constraints may be used to eliminate some of the variables, leaving a problem with only inequality constraints and fewer variables. Even if the equalities are difficult to solve analytically, it may still be worthwhile solving them numerically. This is the approach taken by the generalized reduced gradient method, which is described in Section 8.7. 

The exact analytical approach to the estimation of zj new is practically impossible because of the reasons mentioned above. Therefore to solve the problem we used the method of mathematical experiment, Monte Carlo method. Our aim was ... 

The effort to solve Eqs.(l) evidently depends on the refractive index profile. For isotropic media in a one-dimensional refractive index profile the modes are either transversal-electric (TE) or transversal-magnetic (TM), thus the problem to be solved is a scalar one. If additionally the profile consists of individual layers with constant refractive index, Eq.(l) simplifies to the Flelmholtz-equation, and the solution functions are well known. Thus, by taking into account the relevant boundary conditions at interfaces, semi-analytical approaches like the Transfer-Matrix-Method (TMM) can be used. For two-dimensional refractive index profiles, different approaches can be... 

The basic steps that are taken to solve an analytical problem can be described using the scientific problem-solving approach shown in Figure 2.1. The first step in defining the problem is gaining an understanding of the context of the... 

The PLS approach to multivariate linear regression modeling is relatively new and not yet fully investigated from a theoretical point of view. The results with calibrating complex samples in food analysis 122,123) j y jnfj-ared reflectance spectroscopy, suggest that PLS could solve the general calibration problem in analytical chemistry. 

We are generally concerned with solving real-world engineering problems that have temperature- and composition-dependent fluid properties and chemical complexity. Both of these attributes generally frustrate analytical approaches, which, for practical purposes, usually rely on constant properties and linearity. Therefore numerical solutions will eventually be the only viable alternative for most practical problems. 

This set of equations can be solved by a variety of approaches. Historically they were solved analytically by a separation-of-variables method, which is tedious, time-consuming, and, for most, an error-prone task. The results presented here were computed using a finite-volume discretization of the momentum equation on a 10 by 10 mesh, which was solved iteratively in a spreadsheet. The programming time was a couple of hours, and the solution is found in about a minute on a typical personal computer. The results are accurate to within one percent of the exact series solutions. The details of the spreadsheet programming for this problem are included in an appendix. 

A numerical solution procedure is reasonably flexible in accommodating variations of problems. For example, the Graetz problem could be solved easily for velocity profiles other than the parabolic one. Also variable properties can be incorporated easily. Either of these alternatives could easily frustrate a purely analytical approach. The Graetz problem can also be worked for noncircular duct cross sections, as long as the velocity distribution can be determined as outlined in Section 4.4. 

Following the approach taken by Currie [82], this problem can be solved analytically in terms of exponential integrals. Noting that 2 fdf = df2, Eq. 5.10 can easily be integrated once to produce a second-order equation as... 

In such a representation of an infinite set of master equations for the distribution functions of the state of the surface and of pairs of surface sites (and so on) will arise. This set of equations cannot be solved analytically. To handle this problem practically, this hierarchy must be truncated at a certain level. In such an approach the numerical part needs only a small amount of computer time compared to direct computer simulations. In spite of very simple theoretical descriptions (for example, mean-field approach for certain aspects) structural aspects of the systems are explicitly taken here into account. This leads to results which are in good agreement with computer simulations. But the stochastic model successfully avoids the main difficulty of computer simulations the tremendous amount of computer time which is needed to obtain good statistics for the results. Therefore more complex systems can be studied in detail which may eventually lead to a better understanding of such systems. 

Frank was a master at providing clear, straightforward explanations to problems of great complexity. His articles had the rare combination of perspicuity and perspicacity. As a measure of the perennial impact of Frank s work consider this Throughout his career Frank S. Ham was the author, or co-author, of 64 articles in the last four years alone, these papers have been cited 343 times - a remarkable achievement. I frequently sought his opinion on articles that I had written and more often than not received a reply, which, I think, epitomised his approach to problem solving Nice work, but I am sure this could be solved analytically . 

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