This is a research-oriented course emphasizing on mathematics applied to problems in mechanics. Grades are based on homework (40%), a term project (40%) agreed by the Instructor, in-class oral presentation (10%) on a recent publication and occasional attendance at seminars at NTU Math Center (10%). Lectures include two parts.
Part I
Regular singular & Singular points: asymptotic solutions to singular solutions of ordinary differential equations
Special functions, series and their asymptotic expansions: Bessel, modified Bessel, Airy functions, etc.
Method of stationary phase. Boundary layer matching techniques, WKBJ and multiscale analysis (expansion).
Part II.
Applications of Part I techniques to problems in mechanics: nonlinear dynamics, classical and nano-micro-fluidics.