This book presents mathematical tools to solve partial differential equations, typical of physical problems. It explains in a detailed manner the process of solving the problems that typically arise in the context of physics. Although there are a large number of textbooks on this topic, few go so deep into the topic. One of the original and unique features of this book is emphasis on the mathematical formulation of the problems, as well as the analysis of several alternative ways to solve them. Importantly, the book provides a graphical analysis of the results when appropriate. It describes a wide scope of the problems, with detailed solutions and the methods involved, ranging from cases in one to three dimensions, from Cartesian to polar, cylindrical, and spherical coordinates and includes properties and applications of the Fourier transform to solve partial differential equations.
This book covers the main physical mechanisms and the different contributions (1/f noise, shot noise, etc.) behind electronic fluctuations in various spintronic devices. It presents the first comprehensive summary of fundamental noise mechanisms in both electronic and spintronic devices and is therefore unique in that aspect. The pedagogic introduction to noise is complemented by a detailed description of how one could set up a noise measurement experiment in the lab. A further extensive description of the recent progress in understanding and controlling noise in spintronics, including the boom in 2D devices, molecular spintronics, and field sensing, is accompanied by both numerous bibliography references and tens of case studies on the fundamental aspects of noise and on some important qualitative steps to understand noise in spintronics. Moreover, a detailed discussion of unsolved problems and outlook make it an essential textbook for scientists and students desiring to exploit the information hidden in noise in both spintronics and conventional electronics.
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