MATHEMATICAL ANALYSIS AND NUMERICAL METHODS FOR SCIENCE AND TECHNOLOGY. - Volume 2, Functional and Variational Methods

Chapters III and IV introduce the fundamental tools of functional transforms (Fourier, Hankel, Mellin, fast Fourier transforms and Sobolev spaces). These chapters make use of the theory of distributions (covered in an Appendix). Chapter V examines linear differential operators in a fairly broad framework. The role of characteristics, and the usual classification of linear differential operators as elliptic, parabolic and hyperbolic operators are covered. Chapter VI includes the main ideas for operators in Banach spaces or Hilbert spaces (spaces particularly well adapted to the study of the linear problems of physics and mechanics), and Chapter VII presents basic variational methods.