In the following chapters, we discuss the fundamental basis, procedures, and examples of computer modeling of data by nonlinear regression analysis. We hope to do this in a way that any interested practitioner of chemistry or biochemistry will be able to understand. No advanced mathematical training should be necessary, except for understanding the basics of algebra and elementary calculus.
Nearly all of the methods and applications in this book are suitable for modern (circa 1995) personal computers such as IBM-PCs, their clones, and Macintosh machines. A beginning-to-intermediate level of microcomputer literacy is necessary to use the methods described. An intermediate-level familiarity with computer programming in BASIC or FORTRAN or some knowledge of a suitable general mathematics software package (see Chapter 2) is required for application of the techniques discussed. Although a variety of programming languages could be used, we have focused on BASIC and FORTRAN because of the traditional use and familiarity of these languages in the scientific community. We have also presented a few applications in the Mathcad environment (see Chapter 2) because it is easy to learn and use and is familiar to us.
We now give a brief preview of what is to follow. Chapters 2 to 4 discuss general aspects of using nonlinear regression. Chapter 2 discusses the nature of linear and nonlinear models and algorithms and the operations involved in linear and nonlinear regression. It also provides a brief source list of appropriate mathematics software packages. Chapter 3 is a detailed tutorial on how to construct suitable models for analysis of experimental data. Chapter 4 discusses approaches to solving the problem of correlation between parameters in models and other difficulties in nonlinear regression analysis. This chapter makes use of the concept of graphical error surfaces and shows how their shapes can influence the quality of convergence.
Chapters 5 to 14 present specific selected applications of computer modeling to various experiments used in chemical and biochemical research. Highlights of these chapters include the determination of analyte concentrations by titrations without standardizing the titrant, estimation of electron transfer rate constants and surface concentrations from electrochemical experiments, and the estimation of the secondary structure of proteins from infrared spectroscopic data. These applications chapters include a short review of principles and models for each technique, examples of computer modeling for real and theoretical data sets, and selected examples from the literature specific to each particular instrumental technique.
The examples in Chapters 5 to 14 have been chosen for their tutorial value and because of our own familiarity with the instrumental methods involved. There are many more excellent research applications involving computer modeling of data, which we have not had room to include in this book. We have tried to limit ourselves to illustrative examples compatible with modern personal computers (i.e., circa 1995). We realize, however, that the microcomputer revolution is ongoing. The future should bring to our desktops the capability of analyzing increasingly larger data sets with increasingly more complex models. The reader is directed to several review articles for a taste of future possibilities [6, 7].
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