Yuh-Kang Pan
Boston College Chestnut Hill, Massachusetts 02167
Mathematics for Chemists
Chemistry curricula have undergone substantial changes during the past decade, intended to orient the students toward developments in modern chemistry.' Therefore, nowadays, a senior chemistry major usually has had some introductory courses in quantum chemistry, statistical thermodynamics, etc. Graduate students in all fields of chemistry usually are required or encouraged to take quantum mechanics, statistical mechanics, and chemical kinetics, but a t the same time these students lack some of the basic mathematical background required for such courses. Without a reliable knowledge of such mathematics it is extremely difficult for a student to follow any line of argument in these fields, and it is certainly impossible for him to feel a t home in his research-if this involves application of quantum mechanics or statistical mechanics. To overcome this difficulty, the author organized and taught a course titled "Mathematical Methods of Physical Chemistry." This was a one-semester, threelecture-a-week course and was offered to seniors and first-year graduate students in the chemistry department. The purpose of the course was to fill in the mathematical knowledge gap before offering a suhstantive treatment of quantum mechanics, statistical mechanics, and kinetic theory, etc., and to present mathematical techniques which have proved to be useful in analyzing problems or doing research in chemistry. We assumed that the student has been exposed to calculus, elementary differential equations, and the standard undergraduate chemistry curriculum. Since it was a one-semester course, rather than presenting a broad and superficial survey of the many topics in mathematical physics, we had chose11 to develop a series of selected topics which we believed form the mathematical background of modern chemistry. Seven general topics were covered in this course, namely, linear algebra, functions of complex variables, special functions, integral transforms or operational calculus,
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Journal of Chemical Education
partial differential equations, calculus of variations, and probability theory. The materials presented in this course are a little bit broader in scope and are treated in greater depth than that of Anderson's 'WIathematics for Quantum Chemistry,"z however are a little bit narrower and less sophisticated than Mathews and Walker's "Mathematical Methods of Physics."a The author emphasized physical implications of mathematical concepts and problem solving rather than rigorously providing mathematical theorems. It was a practical approach. I n short, this course was intended to give practice and confidencein dealing with problems arising in chemistry course work and research. After having taken the author's course, the students seemed to have gained some confidence in their ability to deal with mathematical problems in modern chemistry. The author feels that it would he better to extend this course to two semesters. I n so doing we could include more topics such as Green's functions, integral equations, numerical methods, and could discuss each topic in a more extensive manner. I n the first semester, we could present the most elementary and important topics which are generally useful for students in all fields of chemistry. I n the second semester, more advanced topics may he introduced and only physical chemistry and theoretical chemistry students would be required to take the second semester. The author hopes that "Xlathematics for Chemists" will eventually hecome a standard course in the chemistry department as mathematical physics is in the physics department. 'See, for example, "A Chemical Education Symposium on Teaching Physical Chemistry," J. CHEM.EDUC.,42, 188 (1965). ANDKXSON, J. M., "Mathematics for Quantum Chemistry," W. A. Benjamin, Ine., New York, 1966. a MATHBWS, J., AND WALKER, R. L., "Mathematical Methods of Physics," W. A. Benjamin, Inc., New York, 1965.
