Generalized calculus with applications to matter and forces (Q2873812)

The text is the 3rd book in the series Mathematics and Physics for Science and Technology. The main goal of the book is introduction of generalized functions and their applications connected with such notions as Heaviside unit step and Dirac unit impulse. There exist more ways to introduce the generalized functions. The book describes two approaches. In the first approach the generalized function is considered as a nonuniform limit of ordinary functions and in the second approach generalized function is a functional over a set of functions.NEWLINENEWLINE The book is strongly application oriented. The application intension follows a book structure too. It is broken down into 10 chapters. Following explanation procedure ``Tool-application'' odd chapters describe mathematical tools and succeeded even chapters contain appropriate problems types suitable to be solved by the tool. A sufficient content information contain the chapter titles: 1. Limit of a sequence of functions, 2. Shape of a loaded string, 3. Functionals over test functions, 4. Bending of bars and beams, 5. Differential operators and geometry, 6. Axisymmetric flows and four sphere theorems, 7. Convolution reciprocity and adjointness, 8. Electric/Magnetic multipoles and images, 9. Multidimensional harmonic potentials, 10. Twenty examples.NEWLINENEWLINE The language (text, figures) of the book is precise, attractive, inspiring and very readable. The book is strongly recommended for students, teachers, and scientists. It is very good for self-study.