Background & Purpose：

(1) Kinetic theory and fluid dynamics:

(a) Instructor: Kazuo Aoki

(b) Course Outline: brief introduction to kinetic theory of gases, Chapman-Enskog and Hilbert expansions, Sone's generalized slip flow theory (linear theory, weakly nonlinear theory, fully nonlinear theory), ghost effect.

(c) Prerequisite Course(s): Linear algebra and multi-variables calculus.

(d) Grading: Homework will be assigned weekly, and no exam.

(e) Textbook: None. [Reference: Y. Sone, Kinetic Theory and Fluid Dynamics (Birkhauser, 2002); Molecular Gas Dynamics: Theory, Techniques, and Applications (Birkhauser, 2007)]

(2) Introduction to Shock Wave Theory

(a) Instructor: Tai-Ping Liu

(b) Course Outline: weak solutions, entropy conditions, Riemann problem, well-poseness theory, nonlinear waves, non-linear resonance.

(c) Prerequisite Course(s): Linear algebra and multi-variables calculus.

(d) Grading: Homework will be assigned weekly, and no exam.

(e) Textbook: None.