Basic Optics: Principles and Concepts addresses in great detail the basic principles of the science of optics, and their related concepts. The book provides a lucid and coherent presentation of an extensive range of concepts from the field of optics, which is of central relevance to several broad areas of science, including physics, chemistry, and biology. With its extensive range of discourse, the book's content arms scientists and students with knowledge of the essential concepts of classical and modern optics. It can be used as a reference book and also as a supplementary text by students at college and university levels and will, at the same time, be of considerable use to researchers and teachers. The book is composed of nine chapters and includes a great deal of material not covered in many of the more well-known textbooks on the subject. The science of optics has undergone major changes in the last fifty years because of developments in the areas of the optics of metamaterials, Fourier optics, statistical optics, quantum optics, and nonlinear optics, all of which find their place in this book, with a clear presentation of their basic principles. Even the more traditional areas of ray optics and wave optics are elaborated within the framework of electromagnetic theory, at a level more fundamental than what one finds in many of the currently available textbooks. Thus, the eikonal approximation leading to ray optics, the Lagrangian and Hamiltonian formulations of ray optics, the quantum theoretic interpretation of interference, the vector and dyadic diffraction theories, the geometrical theory of diffraction, and similar other topics of basic relevance are presented in clear terms. The presentation is lucid and elegant, capturing the essential magic and charm of physics. All this taken together makes the book a unique text, of major contemporary relevance, in the field of optics. Avijit Lahiri is a well-known researcher, teacher, and author, with publications in several areas of physics, and with a broad range of current interests, including physics and the philosophy of science.

Few artworks have been the subject of more extensive modern interpretation than Melencolia I by renowned artist, mathematician, and scientist Albrecht Durer (1514). And yet, did each of these art experts and historians miss a secret manifesto that Durer included within the engraving? This is the first work to decrypt secrets within Melencolia I based not on guesswork, but Durer's own writings, other subliminal artists that inspired him (i.e., Leonardo da Vinci), the Jewish and Christian Bibles, and books that inspired Durer (De Occulta Philosophia and the Hieorglyphica). To read the covert message of Melencolia I is to understand that Durer was a humanist in his interests in mathematics, science, poetry, and antiquity. This book recognizes his unparalleled power with the burin, his mathematical skill in perspective, his dedication to precise language, and his acute observation of nature. Melencolia I may also be one of the most controversial (and at the time most criminal) pieces of art as it hid Durer's disdain for the hierarchy of the Catholic Church, the Kaiser, and the Holy Roman Empire from the general public for centuries. This book closely ties the origins of philosophy (science) and the work of a Renaissance master together, and will be of interest for anyone who loves scientific history, art interpretation, and secret manifestos.

The book contains a detailed account of numerical solutions of differential equations of elementary problems of Physics using Euler and 2nd order Runge-Kutta methods and Mathematica 6.0. The problems are motion under constant force (free fall), motion under Hooke's law force (simple harmonic motion), motion under combination of Hooke's law force and a velocity dependent damping force (damped harmonic motion) and radioactive decay law. Also included are uses of Mathematica in dealing with complex numbers, in solving system of linear equations, in carrying out differentiation and integration, and in dealing with matrices.

Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear relationships.

Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006.
Requires no preliminary knowledge of graduate and advanced mathematics
Discusses the fundamental results of last 15 years in this theory
Suitable for courses for undergraduate students as well as graduate students and specialists in physics mathematics and other sciences

This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include: The multisymplectic and variational nature of Monge-Ampère equations in dimension four Integrability of fifth-order equations admitting a Lie symmetry algebra Applications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfaces A geometric framework to compare classical systems of PDEs in the category of smooth manifolds Groups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed.

This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.

For a physicist, "noise" is not just about sounds, but refers to any random physical process that blurs measurements, and in so doing stands in the way of scientific knowledge. This book deals with the most common types of noise, their properties, and some of their unexpected virtues. The text explains the most useful mathematical concepts related to noise. Finally, the book aims at making this subject more widely known and to stimulate the interest for its study in young physicists.

The development of man's understanding of planetary motions is the crown jewel of Newtonian mechanics. This book offers a concise but self-contained handbook-length treatment of this historically important topic for students at about the third-year-level of an undergraduate physics curriculum. After opening with a review of Kepler's three laws of planetary motion, it proceeds to analyze the general dynamics of 'central force' orbits in spherical coordinates, how elliptical orbits satisfy Newton's gravitational law, and how the geometry of ellipses relates to physical quantities, such as energy and momentum. Exercises are provided, and derivations are set up in such a way that readers can gain analytic practice by filling in the missing steps. A brief bibliography lists sources for readers who wish to pursue further study on their own.

In the last years there have been great advances in the applications of topology and differential geometry to problems in condensed matter physics. Concepts drawn from topology and geometry have become essential to the understanding of several phenomena in the area. Physicists have been creative in producing models for actual physical phenomena which realize mathematically exotic concepts and new phases have been discovered in condensed matter in which topology plays a leading role. An important classification paradigm is the concept of topological order, where the state characterizing a system does not break any symmetry, but it defines a topological phase in the sense that certain fundamental properties change only when the system passes through a quantum phase transition. The main purpose of this book is to provide a brief, self-contained introduction to some mathematical ideas and methods from differential geometry and topology, and to show a few applications in condensed matter. It conveys to physicists the basis for many mathematical concepts, avoiding the detailed formality of most textbooks.

Domain theory, a subject that arose as a response to natural concerns in the semantics of computation, studies ordered sets which possess an unusual amount of mathematical structure. This book explores its connection with quantum information science and the concept that relates them: disorder. This is not a literary work. It can be argued that its subject, domain theory and quantum information science, does not even really exist, which makes the scope of this alleged 'work' irrelevant. BUT, it does have a purpose and to some extent, it can also be said to have a method. I leave the determination of both of those largely to you, the reader. Except to say, I am hoping to convince the uninitiated to take a look. A look at what? Twenty years ago, I failed to satisfactorily prove a claim that I still believe: that there is substantial domain theoretic structure in quantum mechanics and that we can learn a lot from it. One day it will be proven to the point that people will be comfortable dismissing it as a 'well-known' idea that many (possibly including themselves) had long suspected but simply never bothered to write down. They may even call it "obvious!" I will not bore you with a brief history lesson on why it is not obvious, except to say that we have never been interested in the difficulty of proving the claim only in establishing its validity. This book then documents various attempts on my part to do just that.

This is an introductory textbook on computational methods and techniques intended for undergraduates at the sophomore or junior level in the fields of science, mathematics, and engineering. It provides an introduction to programming languages such as FORTRAN 90/95/2000 and covers numerical techniques such as differentiation, integration, root finding, and data fitting. The textbook also entails the use of the Linux/Unix operating system and other relevant software such as plotting programs, text editors, and mark up languages such as LaTeX. It includes multiple homework assignments.

MESH ist ein mathematisches Video ber vielfl chige Netzwerke und ihre Rolle in der Geometrie, der Numerik und der Computergraphik. Der unter Anwendung der neuesten Technologie vollst ndig computergenierte Film spannt einen Bogen von der antiken griechischen Mathematik zum Gebiet der heutigen geometrischen Modellierung. MESH hat zahlreiche wissenschaftliche Preise weltweit gewonnen. Die Autoren sind Konrad Polthier, ein Professor der Mathematik, und Beau Janzen, ein professioneller Filmdirektor.

Der Film ist ein ausgezeichnetes Lehrmittel f r Kurse in Geometrie, Visualisierung, wissenschaftlichem Rechnen und geometrischer Modellierung an Universit ten, Zentren f r wissenschaftliches Rechnen, kann jedoch auch an Schulen genutzt werden.

This book covers different aspects of umbral calculus and of its more recent developments. It discusses the technical details in depth, including its relevant applications. The book has therefore manyfold scopes to introduce a mathematical tool, not widespread known as it should be; to present a complete account of the relevant capabilities through the use of different examples of applications; to provide a formal bridge between different fields of research in pure and applied.

Differential Quadrature and Differential Quadrature Based Element Methods: Theory and Applications is a comprehensive guide to these methods and their various applications in recent years. Due to the attractive features of rapid convergence, high accuracy, and computational efficiency, the differential quadrature method and its based element methods are increasingly being used to study problems in the area of structural mechanics, such as static, buckling and vibration problems of composite structures and functional material structures. This book covers new developments and their applications in detail, with accompanying FORTRAN and MATLAB programs to help you overcome difficult programming challenges. It summarises the variety of different quadrature formulations that can be found by varying the degree of polynomials, the treatment of boundary conditions and employing regular or irregular grid points, to help you choose the correct method for solving practical problems.

In Thermal Physics: Thermodynamics and Statistical Mechanics for Scientists and Engineers, the fundamental laws of thermodynamics are stated precisely as postulates and subsequently connected to historical context and developed mathematically. These laws are applied systematically to topics such as phase equilibria, chemical reactions, external forces, fluid-fluid surfaces and interfaces, and anisotropic crystal-fluid interfaces. Statistical mechanics is presented in the context of information theory to quantify entropy, followed by development of the most important ensembles: microcanonical, canonical, and grand canonical. A unified treatment of ideal classical, Fermi, and Bose gases is presented, including Bose condensation, degenerate Fermi gases, and classical gases with internal structure. Additional topics include paramagnetism, adsorption on dilute sites, point defects in crystals, thermal aspects of intrinsic and extrinsic semiconductors, density matrix formalism, the Ising model, and an introduction to Monte Carlo simulation. Throughout the book, problems are posed and solved to illustrate specific results and problem-solving techniques.

First published in 1963, Advances in Parasitology contains comprehensive and up-to-date reviews in all areas of interest in contemporary parasitology. Advances in Parasitology includes medical studies of parasites of major influence, such as Plasmodium falciparum and trypanosomes. The series also contains reviews of more traditional areas, such as zoology, taxonomy, and life history, which shape current thinking and applications. The 2013 impact factor is 4.36.