ABSTRACT
This chapter provides students with the mathematical background to understand physical chemical principles and to analyze experiments in biothermodynamics. Assuming a basic knowledge of calculus, the chapter develops key concepts for thermodynamic analysis. After a quick review of single-variable calculus, the chapter describes results from multivariable calculus needed for classical and statistical thermodynamics, most notably, maximizing (and minimizing) multivariable functions, expressing and testing exact (and inexact) differentials, integration of multivariable functions along paths, and understanding factors that result in path independence of integration. The chapter describes methods for analyzing data using least-squares methods, providing an analytical framework for model testing, and for determination of physical parameters from experimental measurements. It develops exact methods for fitting linear models to data, and describes the iterative approach used for fitting nonlinear models. The chapter concludes with a discussion of methods for analyzing the uncertainties in fitted parameter values.
