Mathematical Analysis: Approximation and Discrete ProcessesThis fairly self-contained work embraces a broad range of topics in analysis at the graduate level, requiring only a sound knowledge of calculus and the functions of one variable. A key feature of this lively yet rigorous and systematic exposition is the historical accounts of ideas and methods pertaining to the relevant topics. Most interesting and useful are the connections developed between analysis and other mathematical disciplines, in this case, numerical analysis and probability theory.
How to Guard an Art Gallery and Other Discrete Mathematical Adventures
What is the maximum number of pizza slices one can get by making four straight cuts through a circular pizza? How does a computer determine the best set of pixels to represent a straight line on a computer screen? How many people at a minimum does it take to guard an art gallery? Discrete mathematics has the answer to these -- and many other -- questions of picking, choosing, and shuffling. T. S. Michael's gem of a book brings this vital but tough-to-teach subject to life using examples from real life and popular culture.
Detailed derivation of the Discrete Fourier Transform (DFT) and its associated mathematics, including elementary audio signal processing applications and matlab programming examples.
This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes. It contains an introduction to the model, its systematic derivation and its connection to applications, a subsequent analysis of the existence and the stability of fundamental nonlinear structures in 1, 2 and even 3 spatial lattice dimensions.
It's not a book to dip into. It's more like an intensive course in book-form. In fact it does seem rather that authors simply combined their lecture notes and wrote them up into book form - eg page 22: "That's probably enough for today. Give these ideas a try and let me know how it goes. And speak up in class if you see that we need to go over something". But that doesn't detract (in fact it makes the author appear more human!) and adds to the atmosphere of it being a taught course not a reference book.
