This book is intended to serve as a textbook for courses in engineering physics, and as a reference for researchers in theoretical physics with engineering applications introduced via study projects, which will be useful to researchers in analog and digital signal processing. The material has been drawn together from the author's extensive teaching experience, interpreting the classical theory of Landau and Lifschitz. The methodology employed is to describe the physical models via ordinary or partial differential equations, and then illustrate how digital signal processing techniques based on discretization of derivatives and partial derivatives can be applied to such models.
For upper-level undergraduates and graduate students: an introduction to the fundamentals of quantum mechanics, emphasizing aspects essential to an understanding of solid-state theory. Numerous problems (and selected answers), projects, exercises.
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout.
Deep comprehension of applied sciences requires a solid knowledge of Mathematical Analysis. For most of high level scientific research, the good understanding of Functional Analysis and weak solutions to differential equations is essential. This book aims to deal with the main topics that are necessary to achieve such a knowledge. Still, this is the goal of many other texts in advanced analysis; and then, what would be a good reason to read or to consult this book? In order to answer this question, let us introduce the three Authors. Alberto Ferrero got his degree in Mathematics in 2000 and presently he is researcher in Mathematical Analysis at the Universit`a del Piemonte Orientale. Filippo Gazzola got his degree in Mathematics in 1987 and he is now full professor in Mathematical Analysis at the Politecnico di Milano. Maurizio Zanotti got his degree in Mechanical Engineering in 2004 and presently he is structural and machine designer and lecturer professor in Mathematical Analysis at the Politecnico di Milano. The three Authors, for the variety of their skills, decided to join their expertises to write this book. One of the reasons that should encourage its reading is that the presentation turns out to be a reasonable compromise among the essential mathematical rigor, the importance of the applications and the clearness, which is necessary to make the reference work pleasant to the readers, even to the inexperienced ones. The range of treated topics is quite wide and covers the main basic notions of the scientific research which is based upon mathematical models. We start from vector spaces and Lebesgue integral to reach the frontier of theoretical research such as the study of critical exponents for semilinear elliptic equations and recent problems in fluid dynamics. This long route passes through the theory of Banach and Hilbert spaces, Sobolev spaces, differential equations, Fourier and Laplace transforms, before which we recall some appropriate tools of Complex Analysis. We give all the proofs that have some didactic or applicative interest, while we omit the ones which are too technical or require too high level knowledge. This book has the ambitious purpose to be useful to a broad variety of readers. The first possible beneficiaries are of course the second or third year students of a scientific course of degree: in what follows they will find the topics that are necessary to approach more advanced studies in Mathematics and in other fields, especially Physics and Engineering. This text could be also useful to graduate students who want to start a Ph.D. course: indeed it contains the matter of a multidisciplinary Ph.D. course given by Filippo Gazzola for several years at Politecnico di Milano. Finally, this book could be addressed also to the ones who have already left education far-back but occasionally need to use mathematical tools: we refer both to university professors and their research, and to professionals and designers who want to model a certain phenomenon, but also to the nostalgics of the good old days when they were students. It is precisely for this last type of reader that we have also reported some elementary topics, such as the properties of numerical sets and of the integrals; moreover, every chapter is provided with examples and specific exercises aimed at the involvement of the reader. Let us start immediately inviting the reader to find an “anomaly” among the six formulas appearing in the cover. This book is the translation from Italian of the book ”Elementi di Analisi Superiore per la Fisica e l’Ingegneria”. The translation is due to Ilaria Lucardesi.
The current book, Advanced Fluid Mechanics and Heat Transfer is based on author's four decades of industrial and academic research in the area of thermofluid sciences including fluid mechanics, aero-thermodynamics, heat transfer and their applications to engineering systems. Fluid mechanics and heat transfer are inextricably intertwined and both are two integral parts of one physical discipline. No problem from fluid mechanics that requires the calculation of the temperature can be solved using the system of Navier-Stokes and continuity equations only. Conversely, no heat transfer problem can be solved using the energy equation only without using the Navier-Stokes and continuity equations. The fact that there is no book treating this physical discipline as a unified subject in a single book that considers the need of the engineering and physics community, motivated the author to write this book. It is primarily aimed at students of engineering, physics and those practicing professionals who perform aero-thermo-heat transfer design tasks in the industry and would like to deepen their knowledge in this area. The contents of this new book covers the material required in Fluid Mechanics and Heat Transfer Graduate Core Courses in the US universities. It also covers the major parts of the Ph.D-level elective courses Advanced Fluid Mechanics and Heat Transfer that the author has been teaching at Texas A&M University for the past three decades.
Linking physics fundamentals to modern technology-a highly applied primer for students and engineers Reminding us that modern inventions-new materials, information technologies, medical technological breakthroughs-are based on well-established fundamental principles of physics, Jasprit Singh integrates important topics from quantum mechanics, statistical thermodynamics, and materials science, as well as the special theory of relativity. He then goes a step farther and applies these fundamentals to the workings of electronic devices-an essential leap for anyone interested in developing new technologies. From semiconductors to nuclear magnetic resonance to superconducting materials to global positioning systems, Professor Singh draws on wide-ranging applications to demonstrate each concept under discussion. He downplays extended mathematical derivations in favor of results and their real-world design implication, supplementing the book with nearly 100 solved examples, 120 figures, and 200 end-of-chapter problems. Modern Physics for Engineers provides engineering and physics students with an accessible, unified introduction to the complex world underlying today's design-oriented curriculums. It is also an extremely useful resource for engineers and applied scientists wishing to take advantage of research opportunities in diverse fields.
Handbook of Physics is a veritable toolbox for rapid access to a wealth of physics information for everyday use in problem solving, homework, and examinations. This complete reference includes not only the fundamental formulas of physics but also experimental methods used in practice.
