Common Mathematical Operations in Chemistry

Appendix A Common Mathematical Operations in Chemistry A-1 Appendix B Standard Thermodynamic Values for Selected Substances A-5 Appendix C Equilibrium Constants for Selected Substances A-8 Appendix D Standard Electrode (Half-Cell) Potentials A-14 Appendix E Answers to Selected Problems A-15 Glossary G-1 Credits C-1 Index 1-1... 

Appendix A Common Mathematical Operations in Chemistry A-1 Appendix B Standard Thermodynamic Values for Selected Substances A-5 Appendix C Equilibrium Constants for Selected Substances A-8... 

Many other mathematical operations are commonly used in analytical chemistry, including powers, roots, and logarithms. Equations for the propagation of uncertainty for some of these functions are shown in Table 4.9. 

The difficulties in searching for viable options to address mathematics-related inadequacies increase considerably for the quantum chemistry course. The inadequacy of students familiarity with the mathematics required by that course is a rather common situation for quantum chemistry courses, also in other contexts. The course contents usually make provision for this, by including the development of familiarity with the needed mathematics (operators etc.) into the course. However, the characteristics of the UNIVEN context drastically reduce the viability of such option, because of the gap between students attained familiarity with mathematics, and what would be needed to cope with the mathematics for quantum chemistry. It is therefore opted to maximise the focus on the conceptual aspects and on the description of systems and behaviours, while only few mathematical procedures (e.g. the solution of the Schrodinger equation for the hydrogen atom) are presented, to provide at least some exposure to the ways of proceeding of quantum chemistry. 

The final example listed above proposes that the inverse to the operation of differentiation is known as integration. The field of mathematics which deals with integration is known as integral calculus and, in common with differential calculus, plays a vital role in underpinning many key areas of chemistry. 

Regression mcxlels aim at finding a functional relationship between two or more blocks of variables in the simplest case, when only two blocks are present, regression mcxlels operate by approximating the values in one bl(x k (called the responses or dependent variables, and indicated by the matrix Y) using an opportune mathematical function applied to the variables of the other block (called independent variables or predictors and collected into the matrix X) [2]. In this respect, it must be stressed that, even if the two-block is the most common configuration, many problems in food chemistry are formulated in a way that calls for a multi-block structure. 

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