Senba (Miyazaki U.) and Suzuki (Osaka U.) provide an introduction to applied mathematics in various disciplines. Topics include geometric objects, such as basic notions of vector analysis, curvature and extremals; calculus of variation including isoperimetric inequality, the direct and indirect methods, and numerical schemes; infinite dimensional analysis, including Hilbert space, Fourier series, eigenvalue problems, and distributions; random motion of particles, including the process of diffusion, the kinetic model, and semiconductor device equations; linear and non-linear PDE theories; and the system of chemotaxis. Appendices include a catalog of mathematical theories and commentary on elliptic and parabolic equations and systems of self-interacting particles. Distributed by World Scientific.