Discrete Mechanics

There have been many advances in the theory and applications of discrete distributions in recent years. They can be applied to a wide range of problems, particularly in the health sciences, although a good understanding of their properties is very important. Discrete Distributions: Applications in the Health Sciences describes a number of new discrete distributions that arise in the statistical examination of real examples. For each example, an understanding of the issues surrounding the data provides the motivation for the subsequent development of the statistical models. Provides an overview of discrete distributions and their applications in the health sciences. Focuses on real examples, giving readers an insight into the utility of the models. Describes the properties of each distribution, and the methods that led to their development. Presents a range of examples from the health sciences, including cancer, epidemiology, and demography. Features discussion of software implementation – in SAS, Fortran and R – enabling readers to apply the methods to their own problems. Written in an accessible style, suitable for applied statisticians and numerate health scientists. Software and data sets are made available on the Web. Discrete Distributions: Applications in the Health Sciences provides a practical introduction to these powerful statistical tools and their applications, suitable for researchers and graduate students from statistics and biostatistics. The focus on applications, and the accessible style of the book, make it an excellent practical reference source for practitioners from the health sciences.

A self-contained study of the various applications and developments of discrete distribution theory Written by a well-known researcher in the field, Discrete q-Distributions features an organized presentation of discrete q-distributions based on the stochastic model of a sequence of independent Bernoulli trials. In an effort to keep the book self-contained, the author covers all of the necessary basic q-sequences and q-functions. The book begins with an introduction of the notions of a q-power, a q-factorial, and a q-binomial coefficient and proceeds to discuss the basic q-combinatorics and q-hypergeometric series. Next, the book addresses discrete q-distributions with success probability at a trial varying geometrically, with rate q, either with the number of previous trials or with the number of previous successes. Further, the book examines two interesting stochastic models with success probability at any trial varying geometrically both with the number of trials and the number of successes and presents local and global limit theorems. Discrete q-Distributions also features: Discussions of the definitions and theorems that highlight key concepts and results Several worked examples that illustrate the applications of the presented theory Numerous exercises at varying levels of difficulty that consolidate the concepts and results as well as complement, extend, or generalize the results Detailed hints and answers to all the exercises in an appendix to help less-experienced readers gain a better understanding of the content An up-to-date bibliography that includes the latest trends and advances in the field and provides a collective source for further research An Instructor’s Solutions Manual available on a companion website A unique reference for researchers and practitioners in statistics, mathematics, physics, engineering, and other applied sciences, Discrete q-Distributions is also an appropriate textbook for graduate-level courses in discrete statistical distributions, distribution theory, and combinatorics.

An «applications first» approach to discrete wavelet transformations Discrete Wavelet Transformations provides readers with a broad elementary introduction to discrete wavelet transformations and their applications. With extensive graphical displays, this self-contained book integrates concepts from calculus and linear algebra into the construction of wavelet transformations and their various applications, including data compression, edge detection in images, and signal and image denoising. The book begins with a cursory look at wavelet transformation development and illustrates its allure in digital signal and image applications. Next, a chapter on digital image basics, quantitative and qualitative measures, and Huffman coding equips readers with the tools necessary to develop a comprehensive understanding of the applications. Subsequent chapters discuss the Fourier series, convolution, and filtering, as well as the Haar wavelet transform to introduce image compression and image edge detection. The development of Daubechies filtersis presented in addition to coverage of wavelet shrinkage in the area of image and signal denoising. The book concludes with the construction of biorthogonal filters and also describes their incorporation in the JPEG2000 image compression standard. The author's «applications first» approach promotes a hands-on treatment of wavelet transforma-tion construction, and over 400 exercises are presented in a multi-part format that guide readers through the solution to each problem. Over sixty computer labs and software development projects provide opportunities for readers to write modules and experiment with the ideas discussed throughout the text. The author's software package, DiscreteWavelets, is used to perform various imaging and audio tasks, compute wavelet transformations and inverses, and visualize the output of the computations. Supplementary material is also available via the book's related Web site, which includes an audio and video repository, final project modules, and softwarefor reproducing examples from the book. All software, including the DiscreteWavelets package, is available for use with Mathematica®, MATLAB®, and Maple. Discrete Wavelet Transformations strongly reinforces the use of mathematics in digital data applications, sharpens programming skills, and provides a foundation for further study of more advanced topics, such as real analysis. This book is ideal for courses on discrete wavelet transforms and their applications at the undergraduate level and also serves as an excellent reference for mathematicians, engineers, and scientists who wish to learn about discrete wavelet transforms at an elementary level.

Provides easy learning and understanding of DWT from a signal processing point of view Presents DWT from a digital signal processing point of view, in contrast to the usual mathematical approach, making it highly accessible Offers a comprehensive coverage of related topics, including convolution and correlation, Fourier transform, FIR filter, orthogonal and biorthogonal filters Organized systematically, starting from the fundamentals of signal processing to the more advanced topics of DWT and Discrete Wavelet Packet Transform. Written in a clear and concise manner with abundant examples, figures and detailed explanations Features a companion website that has several MATLAB programs for the implementation of the DWT with commonly used filters “This well-written textbook is an introduction to the theory of discrete wavelet transform (DWT) and its applications in digital signal and image processing.” – Prof. Dr. Manfred Tasche – Institut f?r Mathematik, Uni Rostock Full review at https://zbmath.org/?q=an:06492561

Discrete Signals and Inverse Problems examines fundamental concepts necessary to engineers and scientists working with discrete signal processing and inverse problem solving, and places emphasis on the clear understanding of algorithms within the context of application needs. Based on the original ‘Introduction to Discrete Signals and Inverse Problems in Civil Engineering’, this expanded and enriched version: combines discrete signal processing and inverse problem solving in one book covers the most versatile tools that are needed to process engineering and scientific data presents step-by-step ‘implementation procedures’ for the most relevant algorithms provides instructive figures, solved examples and insightful exercises Discrete Signals and Inverse Problems is essential reading for experimental researchers and practicing engineers in civil, mechanical and electrical engineering, non-destructive testing and instrumentation. This book is also an excellent reference for advanced undergraduate students and graduate students in engineering and science.

A unique approach illustrating discrete distribution theory through combinatorial methods This book provides a unique approach by presenting combinatorial methods in tandem with discrete distribution theory. This method, particular to discreteness, allows readers to gain a deeper understanding of theory by using applications to solve problems. The author makes extensive use of the reduction approach to conditional distributions of independent random occupancy numbers, and provides excellent studies of occupancy and sequential occupancy distributions, convolutions of truncated discrete distributions, and compound and mixture distributions. Combinatorial Methods in Discrete Distributions begins with a brief presentation of set theory followed by basic counting principles. Fundamental principles of combinatorics, finite differences, and discrete probability are included to give readers the necessary foundation to the topics presented in the text. A thorough examination of the field is provided and features: Stirling numbers and generalized factorial coefficients Occupancy and sequential occupancy distributions n-fold convolutions of truncated distributions Compound and mixture distributions Thoroughly worked examples aid readers in understanding complex theory and discovering how theory can be applied to solve practical problems. An appendix with hints and answers to the exercises helps readers work through the more complex sections. Reference notes are provided at the end of each chapter, and an extensive bibliography offers readers a resource for additional information on specialized topics.

Mechanics for the nonmathematician-a modern approach For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for nonmathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics-exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. Geometric Mechanics features illustrative examples and assumes only basic knowledge of Lagrangian mechanics. Of related interest . . . APPLIED DYNAMICS With Applications to Multibody and Mechatronic Systems Francis C. Moon A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics. 1998 (0-471-13828-2) 504 pp. MATHEMATICAL PHYSICS Applied Mathematics for Scientists and Engineers Bruce Kusse and Erik Westwig A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering. 1998 (0-471-15431-8) 680 pp.

Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer. The book features derivations of commonly used differential equations based on the fundamental continuum mechanical concepts encountered in various fields, such as engineering, physics, and geophysics. The book begins with geometric, algebraic, and analytical foundations before introducing topics in kinematics. The book then addresses balance laws, constitutive relations, and constitutive theory. Finally, the book presents an approach to multiconstituent continua based on mixture theory to illustrate how phenomena, such as diffusion and porous-media flow, obey continuum-mechanical principles. Continuum Mechanics: The Birthplace of Mathematical Models features: Direct vector and tensor notation to minimize the reliance on particular coordinate systems when presenting the theory Terminology that is aligned with standard courses in vector calculus and linear algebra The use of Cartesian coordinates in the examples and problems to provide readers with a familiar setting Over 200 exercises and problems with hints and solutions in an appendix Introductions to constitutive theory and multiconstituent continua, which are distinctive for books at this level Continuum Mechanics: The Birthplace of Mathematical Models is an ideal textbook for courses on continuum mechanics for upper-undergraduate mathematics majors and graduate students in applied mathematics, mechanical engineering, civil engineering, physics, and geophysics. The book is also an excellent reference for professional mathematicians, physical scientists, and engineers.

Explore the relationship between quantum mechanics and information-age applications This volume takes an altogether unique approach to quantum mechanics. Providing an in-depth exposition of quantum mechanics fundamentals, it shows how these concepts are applied to most of today's information technologies, whether they are electronic devices or materials. No other text makes this critical, essential leap from theory to real-world applications. The book's lively discussion of the mathematics involved fits right in with contemporary multidisciplinary trends in education: Once the basic formulation has been derived in a given chapter, the connection to important technological problems is summarily described. A book for the information age, Quantum Mechanics: Fundamentals and Applications to Technology promises to become a standard in departments of electrical engineering, applied physics, and materials science, as well as physics. It is an excellent text for senior undergraduate and graduate students, and a helpful reference for practicing scientists, engineers, and chemists in the semiconductor and electronic industries.

Quantum Mechanics: Concepts and Applications provides a clear, balanced and modern introduction to the subject. Written with the student’s background and ability in mind the book takes an innovative approach to quantum mechanics by combining the essential elements of the theory with the practical applications: it is therefore both a textbook and a problem solving book in one self-contained volume. Carefully structured, the book starts with the experimental basis of quantum mechanics and then discusses its mathematical tools. Subsequent chapters cover the formal foundations of the subject, the exact solutions of the Schr?dinger equation for one and three dimensional potentials, time-independent and time-dependent approximation methods, and finally, the theory of scattering. The text is richly illustrated throughout with many worked examples and numerous problems with step-by-step solutions designed to help the reader master the machinery of quantum mechanics. The new edition has been completely updated and a solutions manual is available on request. Suitable for senior undergradutate courses and graduate courses.