The book presents a new method of asymptotic analysis of boundary layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. This part gives also the keys to understand a boundary layer problem and of the methods to construct an approximation.
The second part is devoted to SCEM and its applications in fluid mechanics. The advantages of SCEM are discussed in comparison with the standard method of matched asymptotic expansions.
The book is an introduction to the mathematical modelling and the numerical analysis for computational quantum chemistry. The text is self-consistent: no particular familiarity with the subject nor the mathematical tools is required. Only a basic training in functional analysis is necessary. The models are introduced and discussed. They are analyzed mathematically. The numerical techniques are presented and, when possible, also analyzed. Topics closely related to molecular simulation are also addressed, such as solid state physics, liquid state physics, biology, and materials science. The book can
also be useful for students and researchers of those fields, curious about the mathematical techniques and the numerical strategies.