# krainaksiazek basic physics equations and complex phenomena 20124260

- znaleziono 18 produktów w 4 sklepach

### Basic Physics Equations And Complex Phenomena

**Książki Obcojęzyczne>Angielskie>Mathematics & science>PhysicsKsiążki Obcojęzyczne>Angielskie>Children**

0x005ed8b300000000

Sklep: Gigant.pl

### Selected problems in physics with examples and exercises Politechnika Gdańska

**FIZYKA**

What is physics? The answer to this question has been changing, because physics also changes with time. But physics has always dealt with the basic rules governing the world: the macro-world as well as the world of atoms, electrons and nucleons. Physicists are concerned with various kinds of matter and radiation and their interactions. Their main purpose is to find, understand and use the basic laws that govern the natural world. The foundation of physics is experiment. Experimental observation of the phenomena of nature allows physicists to find the rules and principles that relate these phenomena. This leads to formulation of models and theories, which form our perceptions of the investigated phenomena. Any physical model or theory must always be confronted with experiment. Essential contradictions between a particular model or theory and experimental data are a signal that the model or theory should be corrected or replaced by a new one. This confrontation is a source of development of physics and its continuous approaching a truth of nature. Contemporary physics is a highly developed basic science with many fields, which are the foundation of all engineering and technology. Especially strong relations exist between physics and chemistry. Ever since chemistry ceased to be a purely phenomenological science, chemists not only employ certain laws of physics, but even include some complex and subtle physical phenomena and physics' arcane methods of measurement in their own research. This results in a gradual obliteration of the border line between some branches of chemistry and physics. Spis treści: 1. INTRODUCTION 1.1. The nature of physics 1.2. The language and units. of physics 1.3. How to study physics? Questions and problems 2. FUNDAMENTAL LAWS AND LAWS OF CONSERVATION IN PHYSICS 2.1. The meaning of fundamental laws 2.2. On the laws of conservation in physics 2.2.1. Newton's laws of motion 2.2.2. Conservation of momentum 2.2.3. Conservation of angular momentum 2.3. Work and energy 2.3.1. Definition of work in physics 2.3.2. Energy 2.3.3. The law of conservation of energy 2..3.3.1. Conservation of mechanical energy 2.3.3.2. Conservation of total energy Questions and problems 3. KINETIC THEORY AND LAWS OF THERMODYNAMICS 3.1. The microscopic interpretation of temperature 3.2. Measuring temperature 3.3. Internal energy and equipartition of energy 3.4. Laws of thermodynamics 3.4.1. The first law of thermodynamics 3.4.2. The second law of thermodynamics Questions and problems 4. ELECTROMAGNETIC INTERACTIONS 4.1. Static electric force 4.1.1. Electric charges 4.1.2. Quantization and conservation of charge 4.1.3. Electrical interaction between two charged particles - Coulomb's law 4.1.4. Electrical interactions in a system of several charges 4.2. Electric field 4.2.1. Graphic representation of electric fields 4.3. Gauss's law 4.3.1. Flux of electric field 4.3.2. Gauss's law 4.4. Electric potential and voltage 4.4.1. Electric potential energy 4.4.2. Electric potential 4.5. Capacitance and electric energy storage 4.5.1. Capacitors and capacitance 4.5.2. Energy storage 4.6. Electric current and magnetic force 4.6.1. Electric current 4.6.2. Ohm's law 4.6.3. Magnetic force and magnetic field 4.6.4. Magnetic field of linear current. Ampere's law 4.6.5. Gauss's law for magnetic field 4.7. Electromagnetic induction 4.7.1. Faraday's law of induction 4.7.2. Self-induced emf (? s) 4.8. Maxwell's equations Questions and problems 5. SELECTED PROBLEMS OF MODERN PHYSICS 5.1. The photoelectric effect 5.1.1. Photoelectrons 5.1.2. Fundamental features of the photoelectric effect 5.1.3. Einstein's theory of the photoelectric effect 5.2. Photons and electrons 5.2.1. X-ray photons 5.2.2. The Compton effect 5.3. The Bohr model of the atom of hydrogen 5.3. 1. Bohr's assumptions and postulates 5.3.2. Quantization of electron's total energy5.3.3. Electron jumps 5.3.4. Advantages and limitations of the Bohr model 5.4. Wave-particle duality 5.4.1. De Broglie's hypothesis 5.4.2. Experimental verification of de Broglie's hypothesis Questions and problems 6. NUCLEAR PHYSICS 6.1. Nuclear size and structure 6.1.1. Constituents of the nucleus 6.1.2. Nuclear size 6.1.3. Nuclear forces 6.2. Radioactivity 6.2.1. Kinetics of radioactive decay 6.2.2. Beta decay 6.2.3. Alpha decay 6.2.4. Gamma decay 6.3. Nuclear reactions 6.3.1. General remarks 6.3.2. The fission reaction 6.3.3. Nuclear fusion Questions and problems EXERCISES APPENDIX A. Mathematics A.1. Vector algebra A.2. Derivatives A.3. Integrals APPENDIX B. ENGLISH-POLISH PHYSICS DICTIONARY.

Sklep: ksiegarnia.edu.pl

### Fluid Flow Phenomena Springer Netherlands

**Książki / Literatura obcojęzyczna**

This book deals with the simulation of the incompressible Navier-Stokes equations for laminar and turbulent flows. The book is limited to explaining and employing the finite difference method. It furnishes a large number of source codes which permit to play with the Navier-Stokes equations and to understand the complex physics related to fluid mechanics. §Numerical simulations are useful tools to understand the complexity of the flows, which often is difficult to derive from laboratory experiments. This book, then, can be very useful to scholars doing laboratory experiments, since they often do not have extra time to study the large variety of numerical methods; furthermore they cannot spend more time in transferring one of the methods into a computer language. By means of numerical simulations, for example, insights into the vorticity field can be obtained which are difficult to obtain by measurements. §This book can be used by graduate as well as undergraduate students while reading books on theoretical fluid mechanics; it teaches how to simulate the dynamics of flow fields on personal computers. This will provide a better way of understanding the theory. Two chapters on Large Eddy Simulations have been included, since this is a methodology that in the near future will allow more universal turbulence models for practical applications. The direct simulation of the Navier-Stokes equations (DNS) is simple by finite-differences, that are satisfactory to reproduce the dynamics of turbulent flows. A large part of the book is devoted to the study of homogeneous and wall turbulent flows. §In the second chapter the elementary concept of finite difference is given to solve parabolic and elliptical partial differential equations. In successive chapters the 1D, 2D, and 3D Navier-Stokes equations are solved in Cartesian and cylindrical coordinates. Finally, Large Eddy Simulations are performed to check the importance of the subgrid scale models. Results for turbulent and laminar flows are discussed, with particular emphasis on vortex dynamics. §This volume will be of interest to graduate students and researchers wanting to compare experiments and numerical simulations, and to workers in the mechanical and aeronautic industries.

Sklep: Libristo.pl

### Partial Differential Equations Springer-Verlag New York Inc.

**Książki / Literatura obcojęzyczna**

This book is based on a course I have given five times at the University of Michigan, beginning in 1973. The aim is to present an introduction to a sampling of ideas, phenomena, and methods from the subject of partial differential equations that can be presented in one semester and requires no previous knowledge of differential equations. The problems, with hints and discussion, form an important and integral part of the course. In our department, students with a variety of specialties-notably differen tial geometry, numerical analysis, mathematical physics, complex analysis, physics, and partial differential equations-have a need for such a course. The goal of a one-term course forces the omission of many topics. Everyone, including me, can find fault with the selections that I have made. One of the things that makes partial differential equations difficult to learn is that it uses a wide variety of tools. In a short course, there is no time for the leisurely development of background material. Consequently, I suppose that the reader is trained in advanced calculus, real analysis, the rudiments of complex analysis, and the language offunctional analysis. Such a background is not unusual for the students mentioned above. Students missing one of the "essentials" can usually catch up simultaneously. A more difficult problem is what to do about the Theory of Distributions.

Sklep: Libristo.pl

### Cauchy Problem for Schrödinger Equations LAP Lambert Academic Publishing

**Książki / Literatura obcojęzyczna**

The objective of this monograph is to present the most advanced topics in analysis of mathematical structure in Schrödinger equations. Quantum science becomes important in recent years because we need industrial and electronic applications of microscopic phenomena in quantum computation, quantum communication, and quantum cryptography etc. It is also expected in future that computer scientists apply the result in fundamental theory to the development of quantum devices like quantum computers. The exciting results will be of interest to researchers, graduate and undergraduate students in mathematics, physics and computer science, who are interested in linear Schrödinger type equations and understand the basic methods for analysis of partial differential equations. The author hopes to develop the further research in the relevant fields of mathematical analysis on the Cauchy problems for Schrödinger equations.

Sklep: Libristo.pl

### Fixed point methods for the study of semilinear evolution equations LAP Lambert Academic Publishing

**Książki / Literatura obcojęzyczna**

Partial differential equations is a many-faceted subject. Created to describe the mechanical behavior of objects such as vibrating strings and blowing winds, it has developed into a body of material that interacts with many branches of mathematics, such as differential geometry, complex analysis, and harmonic analysis, as well as a ubiquitous factor in the description and elucidation of problems in mathematical physics. The goal of this work is to make more precise the operator approach for some evolution partial differential equations and extend the theory to semilinear operator systems. More exactly,we shall precise basic properties, such as norm estimation and compactness, for the (linear)solution operator associated to the non-homogeneous linear evolution equations and we shall use them in order to apply the Banach, Schauder and Leray-Schauder theorems to the fixed point problems equivalent to Chaichy-Dirichlet problems for evolution equations. We extend these results to the corresponding semilinear operator system.

Sklep: Libristo.pl

### Mathematical Tools for Physics Dover Publications

**Książki / Literatura obcojęzyczna**

Preface to the Dover Edition Introduction Bibliography 1. Basic Stuff 2. Infinite Series 3. Complex Algebra 4. Differential Equations 5. Fourier Series 6. Vector Spaces 7. Operators and Matrices 8. Multivariable Calculus 9. Vector Calculus 1 10. Partial Differential Equations 11. Numerical Analysis 12. Tensors 13. Vector Calculus 2 14. Complex Variables 15. Fourier Analysis 16. Calculus of Variations 17. Densities and Distributions Index

Sklep: Libristo.pl

### Physics and Chemistry of Solid State Gas Sensor Devices John Wiley & Sons Inc

**Książki / Literatura obcojęzyczna**

Of related interest...LASER IONIZATION MASS ANALYSIS Edited by Akos Vertes, Renaat Gijbels, and Fred Adams Edited by three of the field's leading authorities and featuring contributions from thirteen chemists, this book offers a comprehensive look at the new hardware and investigative possibilities of this form of analysis. The book clearly links theory with applications as well as hardware with hard science. Among topics covered are lasers in mass spectrometry, including instrumentation basic to ion generation for mass analysis; methods of using low and medium laser irradiance; high laser irradiance regime; exotic applications of laser ionization mass spectrometry in space research. 1993 (0-471-53673-3) 584 pp. STATISTICAL METHODS IN ANALYTICAL CHEMISTRY -Peter C. Meier and Richard E. Zund Designed to address the practical day-to-day needs of lab chemists, this practical guide demonstrates the ways in which statistics can be used effectively in analytical work. Chapters 1 and 2 present classical statistical techniques, illustrating them in the context of simple situations. Chapter 3 expands the discussion into ancillary techniques, such as exploratory data analysis, made possible with computing. Chapter 4 presents a number of complex examples that might confront the analyst, while emphasizing the conflicting demands imposed on a possible solution. Chapter 5 presents core sections of programs which complement the equations. Complete with a floppy disk of ready-made programs and data files, here is a clear, real-world introduction to maximizing statistical tools in the lab. 1993 (0-471-58454-1) 352 pp. PHOTOCHEMICAL VAPOR DEPOSITION-J. G. Eden Here is an extremely useful overview of photochemical vapor deposition, both its characteristics and potential. The book focuses on the properties of films that have been created by this versatile method and the conditions under which they are grown. The author works from the position that while photochemical vapor deposition (photo-CVD) is not the solution to all low-temperature deposition methodologies, it does provide an added dimension of flexibility to and control over the growth process and has proven to be valuable for those materials and growth steps in device fabrication that are sensitive to the processing temperature. Whenever applicable, the properties of electronic devices incorporating photo-CVD films are presented and numerous tables detail the deposition parameters as well as electrical and structural properties of the films of specific materials. 1992 (0-471-55083-3) 208 pp. Research and development of solid state gas sensor devices began in the 1950s with several uncoordinated independent efforts. The number and pace of these investigations later accelerated in response to increasing pressure placed on the environment and public health by industrial activities. Since 1970, several thousand articles have been written on the subject, and laboratories around the globe have introduced novel methodologies and devices to address needs associated with particular technological developments. Despite the rapid development of this important new technology, very little has been done to review and coordinate data related to sensor science and technology itself. Physics, Chemistry and Technology of Solid State Gas Sensor Devices focuses on the underlying principles of solid state sensor operation and reveals the rich fabric of interdisciplinary science that governs modern sensing devices. Beginning with some historical and scientific background, the text proceeds to a study of the interactions of gases with surfaces. Subsequent chapters present detailed information on the fabrication, performance, and application of a variety of sensors. Types of sensor devices discussed include: * Gas-sensitive solid state semiconductor sensors * Photonic and photoacoustic gas sensors * Fiber optic sensors * Piezoelectric quartz crystal microbalance sensors * Surface acoustic wave sensors * Pyroelectric and thermal sensors For analytical chemists using solid state sensors in environment-related analysis, and for electrical engineers working with solid state sensors, this book will expand and unify their understanding of these devices, both in theory and practice.

Sklep: Libristo.pl

### Mathematical Handbook for Scientists and Engineers Dover Publications

**Książki / Literatura obcojęzyczna**

Preface Chapter 1. Real and Complex Numbers. Elementary Algebra. 1.1. Introduction. The Real-number System 1.2. "Powers, Roots, Logarithms, and Factorials. Sum and Product Notation" 1.3. Complex Numbers 1.4. Miscellaneous Formulas 1.5. Determinants 1.6. Algebraic Equations: General Theorems 1.7. Factoring of Polynomials and Quotients of Polynomials. Partial Fractions 1.8. "Linear, Quadratic, Cubic, and Quartic Equations" 1.9. Systems of Simultaneous Equations 1.10. "Related Topics, References, and Bibliography" Chapter 2. Plane Analytic Geometry 2.1. Introduction and Basic Concepts 2.2. The Straight Line 2.3. Relations Involving Points and Straight Lines 2.4. Second-order Curves (Conic Sections) 2.5. "Properties of Circles, Ellipses, Hyperbolas, and Parabolas" 2.6. Higher Plane Curves 2.7. "Related Topics, References, and Bibliography" Chapter 3. Solid Analytic Geometry 3.1. Introduction and Basic Concepts 3.2. The Plane 3.3. The Straight Line 3.4. "Relations Involving Points, Planes, and Straight Lines" 3.5. Quadric Surfaces 3.6. "Related Topics, References, and Bibliography" Chapter 4. Functions and Limits. Differential and Integral Calculus 4.1. Introduction 4.2. Functions 4.3. "Point Sets, Intervals, and Regions" 4.4. "Limits, Continuous Functions, and Related Topics" 4.5. Differential Calculus 4.6. Integrals and Integration 4.7. Mean-value Theorems. Values of Indeterminate Forms. Weierstrass's Approximation Theorems. 4.8. "Infinite Series, Infinite Products, and Continued Fractions" 4.9. Tests for the Convergence and Uniform Convergence of Infinite Series and Improper Integrals 4.10. Representation of Functions by Infinite Series and Integrals. Power Series and Taylor's Expansion 4.11. Fourier Series and Fourier Integrals 4.12. "Related Topics, References, and Bibliography" Chapter 5. Vector Analysis 5.1. Introduction 5.2. Vector Algebra 5.3. Vector Calculus: Functions of Scalar Parameter 5.4. Scalar and Vector Fields 5.5. Differential Operators 5.6. Integral Theorems 5.7. Specification of a Vector Field in Terms of Its Curl and Divergence 5.8. "Related Topics, References, and Bibliography" Chapter 6. Curvilinear Coordinate Systems 6.1. Introduction 6.2. Curvilinear Coordinate Systems 6.3. Representation of Vectors in Terms of Components 6.4. Orthogonal Coordinate Systems. Vector Relations in Terms of Orthogonal Components 6.5. Formulas Relating to Special Orthogonal Coordinate Systems 6.6. "Related Topics, References, and Bibliography" Chapter 7. Functions of a Complex Variable 7.1. Introduction 7.2. Functions of a Complex Variable. Regions of the Complex-number Plane 7.3. "Analytic (Regular, Holomorphic) Functions" 7.4. Treatment of Multiple-valued Functions 7.5. Integral Theorems and Series Expansions 7.6. Zeros and Isolated Singularities 7.7. Residues and Contour Integration 7.8. Analytic Continuation 7.9. Conformal Mapping 7.10. Functions Mapping Specified Regions onto the Unit Circle 7.11. "Related Topics, References, and Bibliography" Chapter 8. The Laplace Transformation and Other Functional Transformations 8.1. Introduction 8.2. The Laplace Transformation 8.3. Correspondence between Operations on Object and Result Functions 8.4. Table of Laplace-transform Pairs and Computation of Inverse Laplace Transforms 8.5. "Formal" Laplace Transformation of Impulse-function Terms" 8.6. Some Other Integral Transformations 8.7. "Finite Integral Transforms, Generating Functions, and z Transforms" 8.8. "Related Topics, References, and Bibliography" Chapter 9. Ordinary Differential Equations 9.1. Introduction 9.2. First-order Equations 9.3. Linear Differential Equations 9.4. Linear Differential Equations with Constant Coefficients 9.5. Nonlinear Second-order Equations 9.6. Pfaffian Differential Equations 9.7. "Related Topics, References, and Bibliography" Chapter 10. Partial Differential Equations 10.1. Introduction and Survey 10.2. Partial Differential Equations of the First Order 10.3. "Hyperbolic, Parabolic, and Elliptic Partial Differential Equations. Characteristics." 10.4. Linear Partial Differential Equations of Physics. Particular Solutions. 10.5. Integral-transform Methods 10.6. "Related Topics, References, and Bibliography" Chapter 11. Maxima and Minima and Optimization Problems 11.1. Introduction 11.2. Maxima and Minima of Functions of One Real Variable 11.3. Maxima and Minima of Functions of Two or More Real Variables 11.4. "Linear Programming, Games, and Related Topics" 11.5. Calculus of Variations. Maxima and Minima of Definite Integrals 11.6. Extremals as Solutions of Differential Equations: Classical Theory 11.7. Solution of Variation Problems by Direct Methods 11.8. Control Problems and the Maximum Principle 11.9. Stepwise-control Problems and Dynamic Programming 11.10. "Related Topics, References, and Bibliography" Chapter 12. Definition of Mathematical Models: Modern (Abstract) Algebra and Abstract Spaces 12.1. Introduction 12.2. Algebra of Models with a Single Defining Operation: Groups 12.3. "Algebra of Models with Two Defining Operations: Rings, Fields, and Integral Domains" 12.4. Models Involving More Than One Class of Mathematical Objects: Linear Vector Spaces and Linear Algebras 12.5. Models Permitting the Definition of Limiting Processes: Topological Spaces 12.6. Order 12.7. "Combination of Models: Direct Products, Product Spaces, and Direct Sums" 12.8. Boolean Algebras 12.9. "Related Topics, References, and Bibliography" Chapter 13. Matrices. Quadratic and Hermitian Forms 13.1. Introduction 13.2. Matrix Algebra and Matrix Calculus 13.3. Matrices with Special Symmetry Properties 13.4. "Equivalent Matrices. Eigenvalues, Diagonalization, and Related Topics" 13.5. Quadratic and Hermitian Forms 13.6. Matrix Notation for Systems of Differential Equations (State Equations). Perturbations and Lyapunov Stability Theory 13.7. "Related Topics, References, and Bibliography" Chapter 14. Linear Vector Spaces and Linear Transformations (Linear Operators). Representation of Mathematical Models in Terms of Matrices 14.1. Introduction. Reference Systems and Coordinate Transformations 14.2. Linear Vector Spaces 14.3. Linear Transformations (Linear Operators) 14.4. Linear Transformations of a Normed or Unitary Vector Space into Itself. Hermitian and Unitary Transformations (Operators) 14.5. Matrix Representation of Vectors and Linear Transformations (Operators) 14.6. Change of Reference System 14.7. Representation of Inner Products. Orthonormal Bases 14.8. Eigenvectors and Eigenvalues of Linear operators 14.9. Group Representations and Related Topics 14.10. Mathematical Description of Rotations 14.11. "Related Topics, References, and Bibliography" "Chapter 15. Linear Integral Equations, Boundary-value Problems, and Eigenvalue Problems" 15.1. Introduction. Functional Analysis 15.2. Functions as Vectors. Expansions in Terms of Orthogonal Functions 15.3. Linear Integral Transformations and Linear Integral Equations 15.4. Linear Boundary-value Problems and Eigenvalue Problems Involving Differential Equations 15.5. Green's Functions. Relation of Boundary-value Problems and Eigenvalue Problems to Integral Equations 15.6. Potential Theory 15.7. "Related Topics, References, and Bibliography" Chapter 16. Representation of Mathematical Models: Tensor Algebra and Analysis 16.1. Introduction 16.2. Absolute and Relative Tensors 16.3. Tensor Algebra: Definition of Basic Operators 16.4. Tensor Algebra: Invariance of Tensor Equations 16.5. Symmetric and Skew-Symmetric Tensors 16.6. Local Systems of Base Vectors 16.7. Tensors Defined on Riemann Spaces. Associated Tensors 16.8. Scalar Products and Related Topics 16.9. Tensors of Rank Two (Dyadics) Defined on Riemann Spaces 16.10. The Absolute Differential Calculus. Covariant Differentiation 16.11. "Related Topics, References, and Bibliography" Chapter 17. Differential Geometry 17.1. Curves in the Euclidean Plane 17.2. Curves in the Three-dimensional Euclidean Space 17.3. Surfaces in Three-dimensional Euclidean Space 17.4. Curved Spaces 17.5. "Related Topics, References, and Bibliography" Chapter 18. Probability Theory and Random Processes 18.1. Introduction 18.2. Definition and Representation of Probability Models 18.3. One-dimensional Probability Distributions 18.4. Multidimensional Probability Distributions 18.5. Functions of Random Variables. Change of Variables 18.6. Convergence in Probability and Limit Theorems 18.7. Special Techniques for Solving Probability Theorems 18.8. Special Probability Distributions 18.9. Mathematical Description of Random Processes 18.10. Stationary Random Processes. Correlation Functions and Spectral Densities 18.11. Special Classes of Random Processes. Examples 18.12. Operations on Random Processes 18.13. "Related Topics, References, and Bibliography" Chapter 19. Mathematical Statistics 19.1. Introduction to Statistical Methods 19.2. Statistical Description. Definition and Computation of Random-sample Statistics 19.3. General-purpose Probability Distributions 19.4. Classical Parameter Estimation 19.5. Sampling Distributions 19.6. Classical Statistical Tests 19.7. "Some Statistics, Sampling Distributions, and Tests for Multivariate Distributions" 19.8. Random-process Statistics and Measurements 19.9. Testing and Estimation with Random Parameters 19.10. "Related Topics, References, and Bibliography" Chapter 20. Numerical Calculations and Finite Differences 20.1. Introduction 20.2. Numerical Solution of Equations 20.3. "Linear Simultaneous Equations, Matrix Inversion, and Matrix Eigenvalue Problems" 20.4. Finite Differences and Difference Equations 20.5. Approximation of Functions by Interpolation 20.6. "Approximation by Orthogonal Polynomials, Truncated Fourier Series, and Other Methods" 20.7. Numerical Differentiation and Integration 20.8. Numerical Solution of Ordinary Differential Equations 20.9. "Numerical Solution of Boundary-value Problems, Partial Differential Equations, and Integral Equations" 20.10. Monte-Carlo Techniques 20.11. "Related Topics, References, and Bibliography" Chapter 21. Special Functions 21.1. Introduction 21.2. The Elementary Transcendental Functions 21.3. Some Functions Defined by Transcendental Integrals 21.4. The Gamma Function and Related Functions 21.5. Binomial Coefficients and Factorial Polynomials. Bernoulli Polynomials and Bernoulli Numbers. 21.6. "Elliptic Functions, Elliptic Integrals, and Related Functions" 21.7. Orthogonal Polynomials 21.8. "Cylinder Functions, Associated Legendre Functions, and Spherical Harmonics" 21.9. Step Functions and Symbolic Impulse Functions 21.10. References and Bibliography Appendix A. Formulas Describing Plane Figures and Solids Appendix B. Plane and Spherical Trigonometry "Appendix C. Permutations, Combinations, and Related Topics" Appendix D. Tables of Fourier Expansions and Laplace-transform Pairs "Appendix E. Integrals, Sums, Infinite Series and Products, and Continued Fractions" Appendix F. Numerical Tables Squares Logarithms Trigonometric Functions Exponential and Hyperbolic Functions Natural Logarithms Sine Integral Cosine Integral Exponential and Related Integrals Complete Elliptic Integrals Factorials and Their Reciprocals Binomial Coefficients Gamma and Factorial Functions Bessel Functions Legendre Polynomials Error Function Normal-distribution Areas Normal-curve Ordinates Distribution of t Distribution of x

Sklep: Libristo.pl

### Superlinear Parabolic Problems Birkhäuser

**Książki / Literatura obcojęzyczna**

This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. §The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented.§The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics.

Sklep: Libristo.pl

### Variational and Extremum Principles in Macroscopic Systems Elsevier Science Ltd

**Książki / Literatura obcojęzyczna**

Recent years have seen a growing trend to derive models of macroscopic phenomena encountered in the fields of engineering, physics, chemistry, ecology, self-organisation theory and econophysics from various variational or extremum principles. Through the link between the integral extremum of a functional and the local extremum of a function (explicit, for example, in the Pontryagin's maximum principle variational and extremum principles are mutually related. Thus it makes sense to consider them within a common context. The main goal of the present book is to collect various mathematical formulations and examples of physical reasoning that involve both basic theoretical aspects and applications of variational and extremum approaches to systems of the macroscopic world. The first part of the book is focused on the theory, whereas the second focuses on applications. The unifying variational approach is used to derive the balance or conservation equations, phenomenological equations linking fluxes and forces, equations of change for processes with coupled transfer of energy and substance, and optimal conditions for energy management. This volume offers a unique multidisciplinary synthesis of variational and extremum principles in theory and application. It provides a comprehensive review of current and past achievements in variational formulations for macroscopic processes. It uses Lagrangian and Hamiltonian formalisms as a basis for the exposition of novel approaches to transfer and conversion of thermal, solar and chemical energy.

Sklep: Libristo.pl

### Instabilities and Self-Organization in Materials Oxford University Press

**Książki / Literatura obcojęzyczna**

In materials, critical phenomena such as phase transitions, plastic deformation and fracture are intimately related to self-organization. Understanding the origin of spatio-temporal order in systems far from thermal equilibrium and the selection mechanisms of spatial structures and their symmetries is a major theme of present day research on the structure of continuous matter. Furthermore, the development of methods for producing spatially-ordered and self-assembled microstructure in solids by non-equilibrium methods opens the door to many technological applications. There is an increasing demand for a better understanding of new materials from a more fundamental point of view. In order to describe and understand the behavior of such materials, dynamical concepts related to non-equilibrium phenomena, irreversible thermodynamics, nonlinear dynamics, and bifurcation theory, are required. The generic presence of defects and their crucial influence on pattern formation and critical phenomena in extended systems is now well-established. Similar to observations in hydrodynamical, liquid crystal, and laser systems, defects in materials have a profound effect.We found it thus timely to develop a unified presentation of tools, concepts, and methods that are useful to material scientists and engineers. Although specialized treatments of various topics covered in this book are available, we feel that a comprehensive approach may give the reader a higher vantage point. Hence, emphasis is placed on combining the basic physical, mathematical and computational aspects with technological applications within the material's life-cycle, from processing, degradation to eventual failure. The book is divided into two volumes. The first volume is devoted to the most basic concepts of the physics, mechanics and mathematical theory utilized in the analysis of non-equilibrium materials. The reader is exposed to a rigorous background on material deformation, defect theory, transport processes, and the statistical mechanics and thermodynamics of phase transitions. Mathematical concepts of non-linear dynamics, such as bifurcation and instability theory, the dynamics of complex systems near pattern forming instabilities, the generic aspects of pattern formation, selection and stability are presented.Stochastic and numerical methods used in this field are also introduced. The methods and techniques developed in the first volume are applied in the second volume to specific problems in various advanced technologies. These applications include plastic and fracture instabilities, interfacial morphological instabilities in solidification, crystal growth, electro-deposition, surface instabilities in laser, plasma and chemical vapor processing, and material aging instabilities under irradiation and chemical corrosion attack.

Sklep: Libristo.pl

### Theoretical Microfluidics Oxford University Press

**Książki / Literatura obcojęzyczna**

Microfluidics is a young and rapidly expanding scientific discipline, which deals with fluids and solutions in miniaturized systems, the so-called lab-on-a-chip systems. It has applications in chemical engineering, pharmaceutics, biotechnology and medicine. As the lab-on-a-chip systems grow in complexity, a proper theoretical understanding becomes increasingly important. The basic idea of the book is to provide a self-contained formulation of the theoretical framework of microfluidics, and at the same time give physical motivation and examples from lab-on-a-chip technology. After three chapters introducing microfluidics, the governing equations for mass, momentum and energy, and some basic flow solutions, the following 14 chapters treat hydraulic resistance/compliance, diffusion/dispersion, time-dependent flow, capillarity, electro- and magneto-hydrodynamics, thermal transport, two-phase flow, complex flow patterns and acousto-fluidics, as well as the new fields of opto- and nano-fluidics.Throughout the book simple models with analytical solutions are presented to provide the student with a thorough physical understanding of order of magnitudes and various selected microfluidic phenomena and devices. The book grew out of a set of well-tested lecture notes. It is with its many pedagogical exercises designed as a textbook for an advanced undergraduate or first-year graduate course. It is also well suited for self-study.

Sklep: Libristo.pl

### Generalized Analytic Automorphic Forms in Hypercomplex Space Birkhauser

**Inne 1**

'The aim of this book is to provide a first comprehensive overview of the basic theory of hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces. It gives a summary on the research results obtained over the last five years and establishes a new field within the theory of functions of hypercomplex variables and within analytic number theory.' 'Hypercomplex-analyticity generalizes the concept of complex analyticity in the sense of considering null-solutions to higher dimensional Cauchy-Riemann type systems. Vector- and Clifford algebra-valued Eisenstein and Poincare series are constructed within this framework and a detailed description of their analytic and number theoretical properties is provided. In particular, explicit relationships to higher dimensional vector valued variants of the Riemann zeta function and Dirichlet series are established and a concept of hypercomplex multiplication of lattices is introduced. Applications to the theory of Hilbert spaces with reproducing kernels, to partial differential equations and index theory on some conformally flat manifolds are also included.' The book is directed to researchers as well as to graduate and postgraduate students with interest in the fields of the theory of generalized analytic functions in higher dimensional spaces, analytic number theory, function spaces and boundary value problems of partial differential equations of conformally flat manifolds, and some closely related fields in physics, such as instanton theory and quantum gravity.

Sklep: Albertus.pl

### Elementary Fluid Dynamics Oxford University Press

**Książki / Literatura obcojęzyczna**

The study of the dynamics of fluids is a central theme of modern applied mathematics. It is used to model a vast range of physical phenomena and plays a vital role in science and engineering. This textbook provides a clear introduction to both the theory and application of fluid dynamics, and will be suitable for all undergraduates coming to the subject for the first time. Prerequisites are few: a basic knowledge of vector calculus, complex analysis, and simple methods for solving differential equations are all that is needed. Throughout, numerous exercises (with hints and answers) illustrate the main ideas and serve to consolidate the reader's understanding of the subject. The book's wide scope (including inviscid and viscous flows, waves in fluids, boundary layer flow, and instability in flow) and frequent references to experiments and the history of the subject, ensures that this book provides a comprehensive and absorbing introduction to the mathematical study of fluid behaviour.

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