This is an intermediate level post-calculus text on mathematical and statistical methods, directed toward the needs of chemists. It has developed out of a course that I teach at the University of Massachusetts Dartmouth for thirdyear undergraduate chemistry majors and, with additional assignments, for chemistry graduate students. However, I have designed the book to also serve as a supplementary text to accompany undergraduate physical and analytical chemistry courses and as a resource for individual study by students and professionals in all subfields of chemistry and in related fields such as environmental science, geochemistry, chemical engineering, and chemical physics. I expect the reader to have had one year of physics, at least one year of chemistry, and at least one year of calculus at the university level. While many of the examples are taken from topics treated in upper-level physical and analytical chemistry courses, the presentation is sufficiently self contained that almost all the material can be understood without training in chemistry beyond a first-year general chemistry course.
Mathematics courses beyond calculus are no longer a standard part of the chemistry curriculum in the United States. This is despite the fact that advanced mathematical and statistical methods are steadily becoming more and more pervasive in the chemistry literature. Methods of physical chemistry, such as quantum chemistry and spectroscopy, have become routine tools in all subfields of chemistry, and developments in statistical theory have raised the level of mathematical sophistication expected for analytical chemists. This book is intended to bridge the gap from the point at which calculus courses end to the level of mathematics needed to understand the physical and analytical chemistry professional literature.
Even in the old days, when a chemistry degree required more formal mathematics training than today, there was a mismatch between the intermediatelevel mathematics taught by mathematicians (in the one or two additional math courses that could be fit into the crowded undergraduate chemistry curriculum) and the kinds of mathematical methods relevant to chemists. Indeed, to cover all the topics included in this book, a student would likely have needed to take separate courses in linear algebra, differential equations, numerical methods, statistics, classical mechanics, and quantum mechanics.
Condensing six semesters of courses into just one limits the depth of coverage, but it has the advantage of focusing attention on those ideas and techniques most likely to be encountered by chemists. In a work of such breadth yet of such relatively short length it is impossible to provide rigorous proofs of all results, but I have tried to provide enough explanation of the logic and underlying strategies of the methods to make them at least intuitively reasonable. An annotated bibliography is provided to assist the reader interested in additional detail. Throughout the book there are sections and examples marked with an asterisk (*) to indicate an advanced or specialized topic. These starred sections can be skipped without loss of continuity.