Quanta Matemática e Necessária num Curso Introdutório de Físico-Química? Donald A. McQuarrie - University of California - Davis mquarrie@mcn.org

        Universally it seems that a major obstacle for students of physical chemistry is the fluent use of mathematics. One of the reasons for this difficulty is that the mathematics taught by mathematicians in mathematics courses can often seem to be distantly related to the mathematics that we use to solve physical chemistry problems. Because we deal with physical problems, where functions are almost always continuous and well-behaved, the rigor of the mathematics that we require is far less than that taught in mathematics courses by mathematicians. Most physical scientists treat mathematics as a useful computational tool rather than an intellectual edifice. We already know that the solution exists; we already know that the pressure varies smoothly with the temperature; we already know that the limit as the frequency becomes very small is a well-known classical result; and so on. I maintain that many chemistry students do not feel comfortable with mathematics because of the "excess" rigor of typical mathematics courses, but that the use of the mathematics that is required in an introductory physical chemistry course is 95% confidence and experience and only 5% talent.
        After outlining the basic mathematical topics that are used to solve most of the problems in an introductory physical chemistry course, I shall discuss the use of numerical methods such as the Newton-Raphson method for finding the roots of equations and Simpson's Rule for numerical integration. There can be many rich applications of these methods in a physical chemistry course. Students find these methods to be easy to use and very rewarding.  With the wide-spread availability of personal computers and spreadsheet programs, we no longer should restrict ourselves to solving only quadratic equations and other artificial examples. Students can graph data, explore expressions that fit experimentl data, and plot functions that describe physical behavior. Such "hands on" calculations are an invaluable experience and can bring sometimes dead equations back to life.