An Essay


Book Description







Mathematical Analysis


Book Description

This superb and self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. The wide range of topics covered include the differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This text motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.




Inverse Problems and Optimal Design in Electricity and Magnetism


Book Description

The impact of optimization methods in electromagnetism has been much less than in mechanical engineering and particularly the solution of inverse problems in structural mechanics. This book addresses this omission: it will serve as a guide to the theory as well as the computer implementation of solutions. It is self-contained covering all the mathematical theory necessary.




The Roots of Maxwell’s A Dynamical Theory of the Electromagnetic Field


Book Description

The formulation of Maxwell’s equations completely defines the connection between the electric field and the magnetic field, definitively unifying electricity and magnetism and at the same time providing a theoretical synthesis of all the experimental phenomena connected to these areas. In his revolutionary 1864 memoir where J.C. Maxwell presented his equations, he cites a handful of scientists, which were at the basis of his Theory. This book, in its first part, presents an insight on all these latter scientists, reconstructing the scientific network behind Maxwell’s unification and, in the second part, focuses on the Italians in such a network: Ottaviano Fabrizio Mossotti and Riccardo Felici, with a further insight on the connections between Maxwell and Italy and, in particular, Tuscany.




Mathematics in Victorian Britain


Book Description

With a foreword by Adam Hart-Davis, this book constitutes perhaps the first general survey of the mathematics of the Victorian period. It charts the institutional development of mathematics as a profession, as well as exploring the numerous innovations made during this time, many of which are still familiar today.




Classical and Modern Diffraction Theory


Book Description

Providing geophysicists with an in-depth understanding of the theoretical and applied background for the seismic diffraction method, “Classical and Modern Diffraction Theory” covers the history and foundations of the classical theory and the key elements of the modern diffraction theory. Chapters include an overview and a historical review of classical theory, a summary of the experimental results illustrating this theory, and key principles of the modern theory of diffraction; the early cornerstones of classical diffraction theory, starting from its inception in the 17th century and an extensive introduction to reprinted works of Grimaldi, Huygens, and Young; details of the classical theory of diffractions as developed in the 19th century and reprinted works of Fresnel, Green, Helmholtz, Kirchhoff, and Rayleigh; and the cornerstones of the modern theory including Keller’s geometrical theory of diffraction, boundary-layer theory, and super-resolution. Appendices on the Cornu spiral and Babinet’s principle are also included.