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Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. From the reviews: "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." S. Noelle, Book review, German Math. Soc. "Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.
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The book presents a general overview of mathematical models in the context of evolution. It covers a wide range of topics such as population genetics, population dynamics, speciation, adaptive dynamics, game theory, kin selection, and stochastic processes. Written by leading scientists working at the interface between evolutionary biology and mathematics the book is the outcome of a conference commemorating Charles Darwin's 200th birthday, and the 150th anniversary of the first publication of his book "On the origin of species". Its chapters vary in format between general introductory and state-of-the-art research texts in biomathematics, in this way addressing both students and researchers in mathematics, biology and related fields. Mathematicians looking for new problems as well as biologists looking for rigorous description of population dynamics will find this book fundamental.
Biomathematics -- Congresses. --- Biomathematics. --- Computational Biology -- Congresses. --- Models, Biological -- Congresses. --- Natural history. --- Evolution (Biology) --- Biomathematics --- Biology --- Health & Biological Sciences --- Evolution --- Biology - General --- Mathematical models --- Mathematical models. --- Mathematics --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Mathematical and Computational Biology. --- Genetics and Population Dynamics. --- Applications of Mathematics. --- Genetics --- Math --- Science --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Engineering --- Engineering analysis --- Mathematical analysis
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"The author endeavors to present the concepts and ideas as an alternative to the computational approach, trying to avoid long calculations by stressing the mathematical thoughts behind the statements. . . . many problems [are] stated throughout the book, very often accompanied by hints." —Mathematical Reviews (review of the first edition) "This is a rigorous, logically well-organized textbook presenting basic principles and elementary theory of operators. It is written with great care, gradually increasing in complexity. The forte features of the book are the teaching style, illuminating explanation of numerous delicate points, and detailed presentation of topics. Hence, the book can be warmly recommended to a first work for the study of operator theory . . . it is an admirable work for a modern introduction in operator theory." —Zentralblatt MATH (review of the first edition) This fully revised, updated, and corrected edition of The Elements of Operator Theory includes a significant expansion of problems and solutions used to illustrate the principles of operator theory. Written in a user-friendly, motivating style, it covers the fundamental topics of the field in a systematic fashion while avoiding a formula-calculation approach. The book maintains the logical and linear organization of the title’s first edition, progressing through set theory, algebraic structures, topological structures, Banach spaces, and Hilbert spaces before culminating in a discussion of the Spectral Theorem. Included in the presentation are * More than 300 rigorous proofs, specially tailored to the presentation. * Approximately 150 examples, and several interesting counterexamples that demonstrate the frontiers of an important theorem. * Over 300 problems, with many hints, and 20 pages of additional exercises for the second edition. Throughout, the pedagogical tone and the blend of examples and exercises encourage and challenge the reader to explore fresh approaches to theorems and auxiliary results. A self-contained textbook, The Elements of Operator Theory, Second Edition is an excellent resource for the classroom as well as a self-study reference for researchers. Prerequisites comprise an introduction to analysis and basic experience with functions of a complex variable, which most first-year graduate students in mathematics, engineering, or other formal sciences have already acquired. Measure theory and integration theory are necessary only for the last section of the final chapter.
Electronic books. -- local. --- Operator theory. --- Operator theory --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematics. --- Functional analysis. --- Applied mathematics. --- Engineering mathematics. --- Operator Theory. --- Functional Analysis. --- Applications of Mathematics. --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Engineering --- Engineering analysis --- Mathematical analysis
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I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward end-of-chapter exercises excellent...Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time. —Proceedings of the IEEE It is well produced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one. —Computing Reviews I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets. —Physics Today This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and common-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing. —SIAM Review The first half of the book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field. —Mathematical Reviews The book is indeed what its title promises: A friendly guide to wavelets...In short, Kaiser's book is excellently written and can be considered as one of the best textbooks on this topic presently available...it will enjoy wide distribution among mathematicians and physicists interested in wavelet analysis. —Internationale Mathematische Nachrichten For additional review samples and related material, please visit the author's website at www.wavelets.com.
Electronic books. -- local. --- Wavelets (Mathematics). --- Wavelets (Mathematics) --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Applied Mathematics --- Wavelet analysis --- Mathematics. --- Fourier analysis. --- Applied mathematics. --- Engineering mathematics. --- Physics. --- Applications of Mathematics. --- Signal, Image and Speech Processing. --- Mathematical Methods in Physics. --- Fourier Analysis. --- Harmonic analysis
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This book describes the physics of baseball and softball, assuming that the reader has a background in both physics and mathematics at the high school level. The physics is explained in a conversational style, and illustrated with experimental results obtained both in the laboratory and in the field. Simple equations are also used in order to model the experimental results and to test whether the explanations are actually valid. The subject matter provides an excellent opportunity to explain physics in an interesting manner, given the universal popularity of baseball and softball as pastimes. There is also the interaction between a bat and ball, which is a classic problem in physics involving large forces, short time intervals, momentum, and energy transfer, vibration, rotation, and the different physical properties of the wood (or aluminum) of the bat, and the ball. The flight of the ball through the air is another fascinating example of physics in action, involving the effects of gravity, air resistance and ball spin on the ball trajectory. For those readers who already know quite a bit of physics and who are comfortable with mathematical equations, additional material is provided in the appendices. The book also describes many simple projects for readers who wish to perform their own experiments, whether it is for fun, for a school project, or both. Advance Praise for The Physics of Baseball & Softball “…so compelling that I read every page. Rod has compiled a wonderful selection of insight and discovery to the game...I think it would be a great reference book for a physics teacher to enrich lectures or explain topics.” -Prof. Lloyd Smith, School of Mechanical and Materials Engineering, Washington State University.
Mathematics. --- Physics. --- Surfaces (Physics). --- Physics --- Baseball --- Softball --- Sports --- Physical Sciences & Mathematics --- Physics - General --- Baseball. --- Softball. --- Fast pitch softball --- Fastpitch softball --- Base-ball --- Applied mathematics. --- Engineering mathematics. --- Materials science. --- Physics, general. --- Applications of Mathematics. --- Characterization and Evaluation of Materials. --- Indoor baseball --- Ball games --- Surface chemistry --- Surfaces (Technology) --- Math --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Material science --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics
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This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.
Bioinformatics -- Congresses. --- Bioinformatics. --- Computational Biology -- Congresses. --- Quantum theory -- Congresses. --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Quantum physics. --- Quantum Physics. --- Applications of Mathematics. --- Mechanics --- Thermodynamics --- Mathematics. --- Math --- Science --- Bio-informatics --- Biological informatics --- Biology --- Information science --- Computational biology --- Systems biology --- Data processing --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics
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“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein’s theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.
Physics. --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Relativity (Physics) --- Applied mathematics. --- Engineering mathematics. --- Gravitation. --- Astrophysics. --- Cosmology. --- Classical and Quantum Gravitation, Relativity Theory. --- Applications of Mathematics. --- Astrophysics and Astroparticles. --- Gravitation --- Nonrelativistic quantum mechanics --- Space and time --- Mathematics. --- Math --- Science --- Astronomical physics --- Astronomy --- Cosmic physics --- Deism --- Metaphysics --- Engineering --- Engineering analysis --- Mathematical analysis --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Mathematics --- Properties
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Beyond Einstein’s Gravity is a graduate level introduction to extended theories of gravity and cosmology, including variational principles, the weak-field limit, gravitational waves, mathematical tools, exact solutions, as well as cosmological and astrophysical applications. The book provides a critical overview of the research in this area and unifies the existing literature using a consistent notation. Although the results apply in principle to all alternative gravities, a special emphasis is on scalar-tensor and f(R) theories. They were studied by theoretical physicists from early on, and in the 1980s they appeared in attempts to renormalize General Relativity and in models of the early universe. Recently, these theories have seen a new lease of life, in both their metric and metric-affine versions, as models of the present acceleration of the universe without introducing the mysterious and exotic dark energy. The dark matter problem can also be addressed in extended gravity. These applications are contributing to a deeper understanding of the gravitational interaction from both the theoretical and the experimental point of view. An extensive bibliography guides the reader into more detailed literature on particular topics.
Gravitation. --- Gravitation --- Astronomy & Astrophysics --- Physics --- Astronomy - General --- Astrophysics --- Atomic Physics --- Physical Sciences & Mathematics --- Gravity. --- Astrophysics. --- Mathematics. --- Math --- Astronomical physics --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Astronomy. --- Cosmology. --- Astronomy, Astrophysics and Cosmology. --- Classical and Quantum Gravitation, Relativity Theory. --- Applications of Mathematics. --- Astronomy --- Cosmic physics --- Science --- Geophysics --- Mechanics --- Pendulum --- Engineering --- Engineering analysis --- Mathematical analysis --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Mathematics --- Properties
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This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a good background in ordinary differential equations and would like to learn about the applications. It may also be of interest to applied mathematicians, computational scientists, and engineers. It focuses on key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models. Aside from standard well-posedness results for the initial value problem, it focuses on stability of equilibria via linearization and Lyapunov functions and on Hopf bifurcation. It contains a brief introduction to abstract dynamical systems focused on those generated by delay equations, introducing limit sets and their properties. Differential inequalities play a significant role in applications and are treated here, along with an introduction to monotone systems generated by delay equations. The book contains some quite recent results such as the Poincare-Bendixson theory for monotone cyclic feedback systems, obtained by Mallet-Paret and Sell. The linear chain trick for a special family of infinite delay equations is treated. The book is distinguished by the wealth of examples that are introduced and treated in detail. These include the delayed logistic equation, delayed chemostat model of microbial growth, inverted pendulum with delayed feedback control, a gene regulatory system, and an HIV transmission model. An entire chapter is devoted to the interesting dynamics exhibited by a chemostat model of bacteriophage parasitism of bacteria. The book has a large number of exercises and illustrations. Hal Smith is a Professor at the School of Mathematical and Statistical Sciences at Arizona State University. .
Differential equations. --- 517.91 Differential equations --- Differential equations --- Mathematics. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Biomathematics. --- Partial Differential Equations. --- Mathematical and Computational Biology. --- Applications of Mathematics. --- Differential equations, partial. --- Math --- Science --- Partial differential equations --- Delay differential equations. --- Engineering --- Engineering analysis --- Mathematical analysis --- Biology --- Mathematics --- Differential equations, Partial.
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This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.
Differential equations. --- Engineering mathematics. --- Mathematics. --- System theory. --- Systems, Theory of --- Systems science --- Math --- Engineering --- Engineering analysis --- 517.91 Differential equations --- Differential equations --- Mathematics --- Applied mathematics. --- Ordinary Differential Equations. --- Appl.Mathematics/Computational Methods of Engineering. --- Applications of Mathematics. --- Systems Theory, Control. --- Science --- Mathematical analysis --- Philosophy --- Differential Equations. --- Systems theory. --- Mathematical and Computational Engineering. --- Engineering mathematics
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