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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Methods of Contour Integration

    • 1st Edition
    • Volume 3
    • M. L. Rasulov
    • H. A. Lauwerier + 1 more
    • English
    Methods of Contour Integration contains two parts: (1) a systematic exposition of the computational method for solving boundary and mixed problems, and (2) the contour-integral method for investigating general linear mixed problems. The first part includes formulae for expanding arbitrary vector-valued functions in series from integral residues of solutions of boundary-value problems for systems of ordinary differential equations with discontinuous coefficients. These formulae give residue representations of solutions of the corresponding one-dimensional mixed problems for equations with discontinuous coefficients. The book also explains a computational method of separating the variables which is a generalization of the ordinary method of separating variables to the case of nonself-adjoint operators. In part two, the text discusses one-dimensional mixed problems for equations with discontinuous coefficients. Under regular boundary conditions, it proves the existence of solutions for these problems and the representability of the solutions in the form of contour integrals with a complex parameter. The text points out that the contour-integral method is also applicable to parabolic equations and to equations in which the coefficients are functions of time. The book is ideal for mathematicians, students, and professor of calculus and advanced mathematics.

  • A Correlation Study of Methods of Matrix Structural Analysis

    Report to the 14th Meeting, Structures and Materials Panel Advisory Group for Aeronautical Research and Development, NATO, Paris, France, July 6, 1962
    • 1st Edition
    • Volume 69
    • Richard H. Gallagher
    • English
    A Correlation Study of Methods of Matrix Structural Analysis describes the results of a survey and review of airframe matrix structural analysis. The book also explains concepts of force and displacement, as well as the techniques for determining the force-displacement properties of discrete elements employed in analytical idealizations of structures. The text investigates the results of extensive analyses of multiweb low aspect ratio wings, using past evaluative studies and idealizations contained in reports of the AGARD Structures and Materials Panel. The techniques describe in the Panel and other techniques in matrix structural analysis lead to identical formulations of the governing equations. The differences between various references with respect to idealization are independent of the formulation of the governing equations. The solutions to governing equations are precise solutions for the postulated discrete element system. The book also describes a recommended computer program development using whichever is more appropriate between a force approach or displacement approach to matrix structural analysis. The text is valuable for researchers in structural analysis, aeronautics, applied mechanics, and investigators of aircraft engineering.

  • VLSI Metallization

    • 1st Edition
    • Volume 15
    • Norman G. Einspruch + 2 more
    • English
    VLSI Electronics Microstructure Science, Volume 15: VLSI Metallization discusses the various issues and problems related to VLSI metallization. It details the available solutions and presents emerging trends. This volume is comprised of 10 chapters. The two introductory chapters, Chapter 1 and 2 serve as general references for the electrical and metallurgical properties of thin conducting films. Subsequent chapters review the various aspects of VLSI metallization. The order of presentation has been chosen to follow the common processing sequence. In Chapter 3, some relevant metal deposition techniques are discussed. Chapter 4 presents the methods of VLSI lithography and etching. Conducting films are first deposited at the gate definition step; therefore, the issues related to gate metallization are discussed next in Chapter 5.In Chapter 6, contact metallization is elaborated, and Chapter 7 is devoted to multilevel metallization schemes. Long-time reliability is the subject of Chapter 8, which discusses the issues of contact and interconnect electromigration. GaAs metallization is tackled in Chapter 9. The volume concludes with a general discussion of the functions of interconnect systems in VLSI. Materials scientists, processing and design engineers, and device physicists will find the book very useful.

  • VLSI Electronics Microstructure Science

    • 1st Edition
    • Volume 7
    • Norman G. Einspruch
    • English
    VLSI Electronics: Microstructure Science, Volume 7 presents a comprehensive exposition and assessment of the developments and trends in VLSI (Very Large Scale Integration) electronics. This treatise covers subjects that range from microscopic aspects of materials behavior and device performance to the comprehension of VLSI in systems applications. Each chapter is prepared by a recognized authority. The topics contained in this volume include a basic introduction to the application of superconductivity in high-speed digital systems; the expected impact of VLSI technology on the implementation of AI (artificial intelligence); the limits to improvement of silicon integrated circuits; and the various spontaneous noise sources in VLSI circuits and their effect on circuit operation. Scientists, engineers, researchers, device designers, and systems architects will find the book very useful.

  • Surface and Interface Effects in VLSI

    • 1st Edition
    • Volume 10
    • Norman G. Einspruch + 1 more
    • English
    VLSI Electronics Microstructure Science, Volume 10: Surface and Interface Effects in VLSI provides the advances made in the science of semiconductor surface and interface as they relate to electronics. This volume aims to provide a better understanding and control of surface and interface related properties. The book begins with an introductory chapter on the intimate link between interfaces and devices. The book is then divided into two parts. The first part covers the chemical and geometric structures of prototypical VLSI interfaces. Subjects detailed include, the technologically most important interface, Si-SiO2 and the interplay between interface chemistry and the causes for metal-semiconductor contact behavior, primarily in the III-Vs. The following section deals primarily with the electronic properties of interfaces. Under this section, compound semiconductors, semiconductor-semico... interface, constraints that the microscopic interface places on architectures involving metal-semiconductor (MESFET), "Ohmic" contacts, and the behavior of very small, high-speed devices are discussed extensively. The final chapter shows that the Si - SiO2 interface can play a major role in determining carrier transport when MOSFETS are scaled down to ULSI dimensions. Engineers, designers, and scientists will find the book very useful.

  • VLSI Electronics

    Microstructure Science
    • 1st Edition
    • Volume 4
    • Norman G. Einspruch
    • English
    VLSI Electronics: Microstructure Science, Volume 4 reviews trends for the future of very large scale integration (VLSI) electronics and the scientific base that supports its development. This book discusses the silicon-on-insulator for VLSI and VHSIC, X-ray lithography, and transient response of electron transport in GaAs using the Monte Carlo method. The technology and manufacturing of high-density magnetic-bubble memories, metallic superlattices, challenge of education for VLSI, and impact of VLSI on medical signal processing are also elaborated. This text likewise covers the impact of VLSI technology on the design of intelligent measurement instruments and systems. This volume is valuable to scientists and engineers who wish to become familiar with VLSI electronics, device designers concerned with the fundamental character of and limitations to device performance, systems architects who will be charged with tying VLSI circuits together, and engineers conducting work on the utilization of VLSI circuits in specific areas of application.

  • Lithography for VLSI

    VLSI Electronics Microstructure Science
    • 1st Edition
    • Volume 16
    • Norman G. Einspruch + 1 more
    • English
    VLSI Electronics Microstructure Science, Volume 16: Lithography for VLSI treats special topics from each branch of lithography, and also contains general discussion of some lithographic methods. This volume contains 8 chapters that discuss the various aspects of lithography. Chapters 1 and 2 are devoted to optical lithography. Chapter 3 covers electron lithography in general, and Chapter 4 discusses electron resist exposure modeling. Chapter 5 presents the fundamentals of ion-beam lithography. Mask/wafer alignment for x-ray proximity printing and for optical lithography is tackled in Chapter 6. Chapters 7 and 8 on metrology deal with the characterization of lithography by measurements of various types. Engineers, scientists, and technical managers in the semiconductor industry, and engineering and applied physics faculty and graduate students will find the text very useful.

  • VLSI Electronics

    Microstructure Science
    • 1st Edition
    • Volume 3
    • Norman G. Einspruch
    • English
    VLSI Electronics: Microstructure Science, Volume 3 evaluates trends for the future of very large scale integration (VLSI) electronics and the scientific base that supports its development. This book discusses the impact of VLSI on computer architectures; VLSI design and design aid requirements; and design, fabrication, and performance of CCD imagers. The approaches, potential, and progress of ultra-high-speed GaAs VLSI; computer modeling of MOSFETs; and numerical physics of micron-length and submicron-length semiconductor devices are also elaborated. This text likewise covers the optical linewidth measurements on photomasks and wafers and effects of materials technology and fabrication tolerances on guided-wave optical communication and signal processing. This volume is recommended for scientists and engineers who wish to become familiar with VLSI electronics, device designers concerned with the fundamental character of and limitations to device performance, systems architects who will be charged with tying VLSI circuits together, and engineers conducting work on the utilization of VLSI circuits in specific areas of application.

  • VLSI in Medicine

    • 1st Edition
    • Volume 17
    • Norman G. Einspruch + 1 more
    • English
    VLSI Electronics Microstructure Science, Volume 17: VLSI in Medicine deals with the more important applications of VLSI in medical devices and instruments. This volume is comprised of 11 chapters. It begins with an article about medical electronics. The following three chapters cover diagnostic imaging, focusing on such medical devices as magnetic resonance imaging, neurometric analyzer, and ultrasound. Chapters 5, 6, and 7 present the impact of VLSI in cardiology. The electrocardiograph, implantable cardiac pacemaker, and the use of VLSI in Holter monitoring are detailed in these chapters. The neurostimulator is described in Chapter 8. Chapter 9 discusses both implantable and external drug infusion pumps and describes the use of VLSI in a particular external pump. The last two chapters cover topics that apply to the entire field of medical electronics. Engineers, scientists, medical practitioners and researchers will find the book very useful.

  • VLSI Design

    • 1st Edition
    • Volume 14
    • Norman G. Einspruch
    • English
    VLSI Electronics Microstructure Science, Volume 14: VLSI Design presents a comprehensive exposition and assessment of the developments and trends in VLSI (Very Large Scale Integration) electronics. This volume covers topics that range from microscopic aspects of materials behavior and device performance to the comprehension of VLSI in systems applications. Each article is prepared by a recognized authority. The subjects discussed in this book include VLSI processor design methodology; the RISC (Reduced Instruction Set Computer); the VLSI testing program; silicon compilers for VLSI; and specialized silicon compiler and programmable chip for language recognition. Scientists, engineers, researchers, device designers, and systems architects will find the book very useful.

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