FUNDAMENTALS OF MULTIVARIABLE CALCULUS

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This textbook is carefully designed as an early undergraduate introduction to the calculus of several real variables. The balanced coverage is devoted to limits, continuity, partial derivatives, extrema, the nabla operator, multiple integrals, line integrals, surface integrals, and the fundamental theorems of vector calculus. Engaging and accessible with detailed diagrams and copious worked examples, the presentation is well suited to students pursuing applied fields such as engineering. Multiple integration is motivated intuitively through the calculation of mass. The chapter-end problems provide both drill and challenge. Overall, the book should equip students with the knowledge and confidence needed for subsequent courses. An appendix on hints renders the book suitable for self-study. Prerequisites are limited to single-variable calculus, linear algebra, and analytic geometry. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Preliminaries: Lines, Trajectories, Surfaces, and 3D Figures Contents: Preface About the Authors Preliminaries Differential Calculus Double Integrals Triple Integrals Line Integrals Surface Integrals The Principal Theorems Appendix A: Fields in Curvilinear Coordinates Appendix B: Hints and Answers Index Readership: Undergraduate students in mathematics, science, and engineering, as well as practicing engineers.

Fundamentals of Continuum Mechanics

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This textbook offers a concise yet rigorous treatment of continuum mechanics at the introductory level. It differs from traditional textbooks by combining tensor analysis with mechanical analysis and teaching the former's basics within a single chapter. Readers of this book are not required to have learned tensor analysis in the context of engineering mathematics beforehand. The basic objectives of continuum mechanics are included in this textbook to facilitate an easy and thorough understanding of the concepts of continuum mechanics and elasticity. In addition, the mathematics and physics of deformation and kinematics are introduced and studied from the concept of stretch rather than from the traditional approach of strain. The large deformation problem of new smart soft materials is also introduced. This textbook provides illustrative examples and problem sets that enable readers to test their understanding of the subject matter and utilize the tools developed in the formulation of engineering problems. It is suitable for students whose undergraduate disciplines are non-mechanics-related fields. It also helps students or engineers who use the finite element method (FEM) to analyze problems to interpret the results produced by FEM software. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Introduction Contents: Introduction Mathematical Fundamentals: Vectors and Tensors Kinematics of a Continuum Stress Measures The Fundamental Laws of Continuum Mechanics The Constitutive Equations of Continuum Constitutive Models of Soft Materials: Hydrogels and Shape Memory Polymers Applications of Continuum Mechanics Readership: Undergraduate and postgraduate students, and professional engineers interested in learning about continuum mechanics, particularly those from non-mechanics-related disciplines.

FUNDAMENTALS OF QUANTUM MATERIALS

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Despite a long tradition of sophisticated, creative materials synthesis among quantum materials researchers, a sense of broader community has been lacking. In initiating the Fundamentals of Quantum Materials Winter School held annually at the University of Maryland, we wanted to bring together the next generation of growers to learn techniques and pointers directly from senior scientists, and it turns out that we were not alone. The enthusiasm from both students and teachers has been both gratifying and invigorating. Four schools later, we can confidently say that physicists, chemists, and materials scientists, experimentalists and theorists alike, all want to know how to make a good sample. With this in mind, we asked our lecturers to record their most important ideas and share their expertise with a broader audience. This resource is a compilation of fundamental and practical guides on the modern methods of materials synthesis utilized by these experts. We hope that you enjoy reading their essential guidance and state-of-the-art techniques as you explore the Fundamentals of Quantum Materials.

Fundamentals of Quantum Information Extended Edition

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This expanded version to the 2010 edition features quantum annealing algorithm and its application for optimization problems. Recent progress on quantum computing, especially, advanced topics such as Shor's algorithm, quantum search, quantum cryptography and architecture of quantum bit are also included. Book is self-contained and unified in its description of the cross-disciplinary nature of this field. It is not strictly mathematical, but aims to provide intuitive and transparent ideas of the subjects. The book starts from basic quantum mechanics and EPR pair and its measurements. Fundamental concepts of classical computer are given in order to extend it to quantum computer. Classical information theory is also explained in detail such as Shannon and Von Neumann entropy. Then quantum algorithm is introduced starting from Dutch-Josza and ending up with Shor's factorization algorithms. Quantum cryptography is also introduced such as BB84 Protocol, B92 protocol and E91 protocol. Eventually quantum search algorithm is explained. In summary, the book starts from basic quantum mechanics and eventually comes up to state-of-the art quantum algorithm of quantum computations and computers. Students can obtain practical problem-solving ability by attempting the exercises at the end of each chapter. Detailed solutions to all problems are provided.