Senba Takasi, Suzuki Takashi. Applied Analysis. Mathematica Methods in Natural Science

Imperial College Press, 2004. — 393 p. — ISBN: 1-86094-440-X.This book is intended to be an introduction to mathematical science, particularly the theoretical study from the viewpoint of applied analysis. As basic materials, vector analysis and calculus of variation are taken, and then Fourier analysis is introduced for the eigenfunction expansion to justify. After that, statistical method is presented to control the mean field of many particles, and the mathematical theory to linear and nonlinear partial differential equations is accessed. System of chemotaxis is a special topic in this book, and well-posedness of the model is established. We summarize several mathematical theories and give some references for the advanced study. We also picked up some materials from classical mechanics, geometry, mathematical programming, numerical schemes, and so forth. Thus, this book covers some parts of undergraduate courses for mathematical study. It is also suitable for the first degree of graduate course to learn the basic ideas, mathematical techniques, systematic logic, physical and biological motivations, and so forth.
Most part of this monograph is based on the notes of the second author for undergraduate and graduate courses and seminars at several universities.