Books by Prem K. Kythe

Due to the growing need of introduction of numerical methods in engineering to solve boundary value problems, many engineering and mathematics graduate curricula now include courses in both finite and boundary element methods. Traditionally numerical methods have always been mathematically oriented.

This book discusses the mathematical analysis created around the Bieberbach conjecture, which is responsible for the development of many beautiful aspects of complex analysis, especially in the geometric-function theory of univalent functions. The book covers novel techniques for solving problems in the complex plane, proves the de Branges theor

A Complete Treatment of Current Research Topics in Fourier Transforms and Sinusoids Sinusoids: Theory and Technological Applications explains how sinusoids and Fourier transforms are used in a variety of application areas, including signal processing, GPS, optics, x-ray crystallography, radioastronomy, poetry and music as sound waves, and the medical sciences. With more than 200 illustrations, the book discusses electromagnetic force and sychrotron radiation comprising all kinds of waves, including gamma rays, x-rays, UV rays, visible light rays, infrared, microwaves, and radio waves. It also covers topics of common interest, such as quasars, pulsars, the Big Bang theory, OlbersΓÇÖ paradox, black holes, Mars mission, and SETI.The book begins by describing sinusoidsΓÇöwhich are periodic sine or cosine functionsΓÇöusing well-known examples from wave theory, including traveling and standing waves, continuous musical rhythms, and the human liver. It next discusses the Fourier series and transform in both continuous and discrete cases and analyzes the Dirichlet kernel and Gibbs phenomenon. The author shows how invertibility and periodicity of Fourier transforms are used in the development of signals and filters, addresses the general concept of communication systems, and explains the functioning of a GPS receiver. The author then covers the theory of Fourier optics, synchrotron light and x-ray diffraction, the mathematics of radioastronomy, and mathematical structures in poetry and music. The book concludes with a focus on tomography, exploring different types of procedures and modern advances. The appendices make the book as self-contained as possible.

This book discusses the mathematical analysis created around the Bieberbach conjecture, which is responsible for the development of many beautiful aspects of complex analysis, especially in the geometric-function theory of univalent functions. The book covers novel techniques for solving problems in the complex plane, proves the de Branges theor

This self-contained text provides a sufficient theoretical basis to understand Green¿s function method, which is used to solve initial and boundary value problems involving linear ODEs and PDEs. It presents a variety of approaches, including classical and general variations of parameters, Wronskian method, Bernoulli¿s separation method, integral transform method, method of images, conformal mapping method, and interpolation method. The text also covers applications of Green¿s functions and contains numerous examples and exercises from diverse areas of mathematics, applied science, and engineering.

Many engineering and mathematics graduate curricula include a course in boundary element methods. Such a course must cover numerical methods, basic methodology to real problems, and interactive computer usage. This textbook provides both theory and applications, necessary for applied courses.