Many mathematics departments usually teach a variety of courses for students from different science departments and even from different faculties. These "service" courses are usually taught in the same way as the courses for mathematics major students. However, in science, because of the need to better analyse and interpret experimental data and the increased use of mathematical tools in chemistry and geology textbooks, it is becoming necessary to teach these science students quantitative skills beyond the scope of first year mathematics courses. This paper describes the design of a one-semester second year mathematics course, mainly for chemistry and geology students, with three specific objectives: to develop students' ability to quantitatively analyse problems arising in their own field, to illustrate the great utility of mathematical models to provide answers to key chemistry and geology problems, to develop students' appreciation of the diversity of mathematical approaches potentially useful in the chemical and geological sciences.