This course covers a variety of mathematical methods used in the sciences, focusing particularly on the solution of ordinary and partial differential equations. In addition to calling attention to certain special equations that arise frequently in the study of waves and diffusion, we develop general techniques such as looking for series solutions and, in the case of nonlinear equations, using phase portraits and linearizing around fixed points. We study some simple numerical techniques for solving differential equations. A series of optional sessions in TrueBasic will be offered for students who do not already have a background in programming. Format: lecture, three hours per week. Evaluation will be based on weekly problem sets, a midterm exam and a final exam, all of which have a substantial quantitative component. Prerequisites: Mathematics 105 and familiarity with Newtonian mechanics at the level of Physics 131. No enrollment limit (expected: 20). This is a quantitative/formal reasoning course.