This course develops the basic geometric, algebraic, and computational foundations of vector spaces and matrices and applies them to a wide range of problems and models. The material will be accessible to students who have taken at least one semester of calculus and is useful to most consumers of mathematics. The course focuses on real finite dimensional vector spaces and inner product spaces, although abstract and infinite-dimensional vector spaces will be discussed towards the end of the semester. Applications will be made to computer graphics, environmental models, differential equations, Fourier series, and physics. Computers will be used throughout. Problem sets will be assigned for almost every class. Prerequisite: a year of Calculus.
Calculus provides the language and some powerful tools for the study of change. As such, it is an essential subject for those interested in growth and decay processes, motion, and the determination of functional relationships in general. Using student-selected models from primary literature, we will investigate dynamical systems from economics, ecology, epidemiology and physics. Computers are essential tools in the exploration of such processes and will be integral to the course. No previous programming experience is required. Topics will include: 1) dynamical systems, 2) basic concepts of calculus-- rate of change, differentiation, limits, 3) differential equations, 4) computer programming, simulation, and approximation, 5) exponential and circular functions. While the course is self-contained, students are strongly urged to follow it up by taking NS 316-Linear Algebra or NS 261-Calculus II to further develop their facility with the concepts. In addition to regular substantial problem sets, each student will apply the concepts to recently published models of their choosing.
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