ME 7205 Advanced Mathematical Methods for （我7205先进的数学方法）.pdfVIP

DEPARTMENT OF MECHANICAL AND INDUSTRIAL ENGINEERING ME 7205 Advanced Mathematical Methods for Mechanical Engineers CATALOG DESCRIPTION ME 7205 Advanced Mathematical Methods for Mechanical Engineers (4SH) Topics include complex variables; generalized functions; integral transforms (including Fourier transforms); variational calculus and applications; approximate methods of engineering analysis including asymptotic expansions and regular and singular perturbation methods; and numerical solution of partial differential equations with emphasize on parabolic and elliptic problems occurring in mechanical engineering. Examples are drawn from solid mechanics, vibration, and fluid mechanics. Prerequisite: ME 6200. COURSE DISCUSSION As the catalog description implies this is a multifaceted course, the most advanced in the sequence of mathematics methods courses for MEs. Although the first (or equivalent) course is a prerequisite, it is really a graduate level of mathematical maturity that is required, since the course will be largely self-contained. I will attempt to treat the topics listed in the catalog description in a connected way (except for variational and numerical methods) tying them all to complex analysis. The course will begin with a development of the main ideas behind functions of a complex variable, including complex algebra, simple functions, elementary transcendental functions and series, the integral theorems, contour integration in the complex plane, and integral transforms as applied to ordinary and partial differential equations. Generalized functions will also be covered, including their Fourier transforms. This portion of the course will cover 9-10 w