It was with the publication of Norbert Wiener's book ''The Fourier In­ tegral and Certain of Its Applications" [165] in 1933 by Cambridge Univer­ sity Press that the mathematical community came to realize that there is an alternative approach to the study of c1assical Fourier Analysis, namely, through the theory of c1assical orthogonal polynomials. Little would he know at that time that this little idea of his would help usher in a new and exiting branch of c1assical analysis called q-Fourier Analysis. Attempts at finding q-analogs of Fourier and other related transforms were made by other authors, but it took the mathematical insight and instincts of none other then Richard Askey, the grand master of Special Functions and Orthogonal Polynomials, to see the natural connection between orthogonal polynomials and a systematic theory of q-Fourier Analysis. The paper that he wrote in 1993 with N. M. Atakishiyev and S. K Suslov, entitled "An Analog of the Fourier Transform for a q-Harmonic Oscillator" [13], was probably the first significant publication in this area. The Poisson k~rnel for the contin­ uous q-Hermite polynomials plays a role of the q-exponential function for the analog of the Fourier integral under considerationj see also [14] for an extension of the q-Fourier transform to the general case of Askey-Wilson polynomials. (Another important ingredient of the q-Fourier Analysis, that deserves thorough investigation, is the theory of q-Fourier series.

Mathematics for Biomedical Physics is an open access peer-reviewed textbook geared to introduce several mathematical topics at the rudimentary level so that students can appreciate the applications of mathematics to the interdisciplinary field of biomedical physics. Most of the topics are presented in their simplest but rigorous form so that students can easily understand the advanced form of these topics when the need arises. Several end-of-chapter problems and chapter examples relate the applications of mathematics to biomedical physics. After mastering the topics of this book, students would be ready to embark on quantitative thinking in various topics of biology and medicine.

The principal aim in writing this book has been to provide an intro­ duction, barely more, to some aspects of Fourier series and related topics in which a liberal use is made of modem techniques and which guides the reader toward some of the problems of current interest in harmonic analysis generally. The use of modem concepts and techniques is, in fact, as wide­ spread as is deemed to be compatible with the desire that the book shall be useful to senior undergraduates and beginning graduate students, for whom it may perhaps serve as preparation for Rudin's Harmonic Analysis on Groups and the promised second volume of Hewitt and Ross's Abstract Harmonic Analysis.

This study guide is designed for students taking courses in differential equations. The textbook includes examples, questions, and exercises that will help engineering students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve student’s problem-solving skills and basic and advanced understanding of the topics covered in electric circuit analysis courses.

In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets.

This revised textbook fully updates its comprehensive coverage of Fourier transform, convolution, and definitions of autocorrelation and power spectral density.