Books: 'Partial derivatives'

1

Mashreghi, Javad. Derivatives of Inner Functions. New York, NY: Springer New York, 2013.

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2

D, Beritić-Stahuljak, Valic F, World Health Organization, and United Nations Environment Programme, eds. Partially halogenated chlorofluorocarbons (methane derivatives). Geneva: World Health Organization, 1991.

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3

The oblique derivative problem: The Poincaré-problem. Berlin: Wiley-VCH, 2000.

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4

V, Uspenskiĭ S., ed. Partial differential equations and systems not solvable with respect to the highest-order derivative. New York: Marcel Dekker, 2003.

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5

Berman, Donald. Inactivation of particle-associated coliforms by chlorine and monochloramine. [Washington, D.C.?: U.S. Environmental Protection Agency, 1988.

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6

Berman, Donald. Inactivation of particle-associated coliforms by chlorine and monochloramine. [Washington, D.C.?: U.S. Environmental Protection Agency, 1988.

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7

Berman, Donald. Inactivation of particle-associated coliforms by chlorine and monochloramine. [Washington, D.C.?: U.S. Environmental Protection Agency, 1988.

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8

Berman, Donald. Inactivation of particle-associated coliforms by chlorine and monochloramine. [Washington, D.C.?: U.S. Environmental Protection Agency, 1988.

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9

Berman, Donald. Inactivation of particle-associated coliforms by chlorine and monochloramine. [Washington, D.C.?: U.S. Environmental Protection Agency, 1988.

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10

Berman, Donald. Inactivation of particle-associated coliforms by chlorine and monochloramine. [Washington, D.C.?: U.S. Environmental Protection Agency, 1988.

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11

Chaplin, David A. The application of biotransformations to the synthesis of partially protected sugar derivatives. [s.l.]: typescript, 1991.

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12

T, Smith Robert. Calculus: Late transcendental functions. 4th ed. New York, NY: McGraw-Hill, 2012.

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13

1980-, Moradifam Amir, ed. Functional inequalities: New perspectives and new applications. Providence, Rhode Island: American Mathematical Society, 2013.

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14

Finite difference methods in financial engineering: A partial differential equation approach. Chichester, UK: Wiley, 2007.

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15

Biblical names: A literary study of Midrashic derivations and puns. Ramat Gan: Bar-Ilan University Press, 1991.

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16

Duffy, Daniel J. Finite Difference Methods in Financial Engineering. New York: John Wiley & Sons, Ltd., 2006.

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17

Igusa, Kiyoshi, 1949- editor of compilation, Martsinkovsky, A. (Alex), editor of compilation, and Todorov, G. (Gordana), editor of compilation, eds. Expository lectures on representation theory: Maurice Auslander Distinguished Lectures and International Conference, April 25-30, 2012, Woods Hole Oceanographic Institute, Quissett Campus, Falmouth, MA. Providence, Rhode Island: American Mathematical Society, 2014.

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18

Wigderson, Avi, Xi Chen, and Neeraj Kayal. Partial Derivatives in Arithmetic Complexity and Beyond. Now Publishers, 2011.

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19

Mashreghi, Javad. Derivatives of Inner Functions. Springer, 2014.

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20

T, Patera Anthony, Peraire Jaume, and Langley Research Center, eds. A posteriori finite element bounds for sensitivity derivatives of partial-differential-equation outputs. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1998.

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21

Derivatives of Inner Functions Fields Institute Monographs. Springer, 2012.

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22

Mann, Peter. Matrices. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0031.

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This chapter looks at the calculus of a function of two or more variables, which is the subject of partial differentiation. The partial derivative of a function is the rate of change of the function with respect to the distance in the direction of a particular coordinate axis and is symbolised with the sign ∂. The chapter spends time on the implicit function theorem, since it is relied upon heavily elsewhere in the text. Lagrange multipliers are used to solve constrained optimisation problems. Topics include critical points, the product rule, the chain rule, directional derivatives, hypersurfaces and Taylor’s theorem. In addition, the chapter discusses Jacobian matrices, the inverse function theorem, gradients, level sets and Hessian matrices.

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23

Estep, Donald, K. Eriksson, and Johnson C. Applied Mathematics Body and Soul, Volume 1: Derivatives and Geometry in R3. Springer, 2003.

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24

Boudreau, Joseph F., and Eric S. Swanson. Ordinary differential equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0011.

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This chapter surveys the ordinary differential equations (ODEs) that occur in classical and quantum mechanics, and describes both numerical algorithms and appropriate software design for solving them. Systems of ordinary differential equations, together with a few constants of integration, can in most cases be regarded as a means of defining a function (the “solution”). In this chapter, we develop an object-oriented architecture that applies integrators of the Runge-Kutta family to create these functions. Together with an automatic derivative system for generating partial derivatives from functions of one or more variables, the differential equation solver becomes a powerful tool for solving a variety of few-body problems in classical Hamiltonian systems. This chapter presents a blend of numerical algorithms, physics, and computing techniques. The phenomenon of energy drift is discussed and used to motivate symplectic solvers. Techniques such as adaptive step size and possible problems with stability and multiple scales are also discussed.

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25

D, Beritic-Stahuljak, Millischer R, Valic F, International Program on Chemical Safety., United Nations Environment Programme, and World Health Organization, eds. Partially halogenated chlorofluorocarbons (ethane derivatives). Geneva: World Health Organization, 1992.

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26

Sherwood, Dennis, and Paul Dalby. Thermodynamics and mathematics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782957.003.0004.

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Most school mathematics is about how one variable, y, varies with respect to one other variable, x, according to an equation such as y = 3x2. Equations like this underpin the student’s knowledge of algebra, and differential and integral calculus. Thermodynamics, however, is necessarily about how a variable, such as the pressure P, varies with respect not to one but to three variables simultaneously – for example, the mole number n, the volume V, and the temperature T. This makes the algebra of thermodynamics more complex, and also implies that mutual changes between pairs of variables is described not in terms of total derivatives of the form dy/dx, but rather by partial derivatives of the form (∂P/∂T)V. Many students find the leap from dy/dx to (∂P/∂T)V very difficult - the purpose of this chapter is therefore to build the reader’s confidence in understanding, and manipulating, functions of two and three variables.

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27

Lieberman, Gary M. Oblique Derivative Problems for Elliptic Equations. World Scientific Publishing Co Pte Ltd, 2013.

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28

Discrete Variational Derivative Method A Structurepreserving Numerical Method For Partial Differential Equations. CRC Press, 2010.

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29

Furihata, Daisuke, and Takayasu Matsuo. Discrete Variational Derivative Method: A Structure-Preserving Numerical Method for Partial Differential Equations. Taylor & Francis Group, 2010.

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30

Botsford, Louis W., J. Wilson White, and Alan Hastings. Population Dynamics for Conservation. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198758365.001.0001.

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This book is a quantitative exposition of our current understanding of the dynamics of plant and animal populations, with the goal that readers will be able to understand, and participate in the management of populations in the wild. The book uses mathematical models to establish the basic principles of population behaviour. It begins with a philosophical approach to mathematical models of populations. It then progresses from a description of models with a single variable, abundance, to models that describe changes in the abundance of individuals at each age, then similar models that describe populations in terms of the abundance over size, life stage, and space. The book assumes a knowledge of basic calculus, but explains more advanced mathematical concepts such as partial derivatives, matrices, and random signals, as it makes use of them. The book explains the basis of the principles underlying important population processes, such as the mechanism that allow populations to persist, rather than go extinct, the way in which populations respond to variable environments, and the origin of population cycles.The next two chapters focus on application of the principles of population dynamics to manage for the prevention of extinction, as well as the management of fisheries for sustainable, high yields. The final chapter recapitulates how different population behaviors arise in situations with different levels of density dependence and replacement (the potential lifetime reproduction per individual), and how variability arises at different time scales set by a species’ life history.

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31

author, Mazʹi︠a︡ V. G., ed. Maximum principles and sharp constants for solutions of elliptic and parabolic systems. 2012.

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32

Chen, Yu. Applications of partially fluorinated binaphthol ligands in asymmetric catalysis and synthesis of alpha-amino acid derivatives. 2005.

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33

Rajeev, S. G. Vector Fields. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0001.

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The velocity of a fluid at each point of space-time is a vector field (or flow). It is best to think of it in terms of the effect of fluid flow on some scalar field. A vector field is thus a first order partial differential operator, called the material derivative in fluid mechanics. The path of a speck of dust carried along (advected) by the fluid is the integral curve of the velocity field. Even simple vector fields can have quite complicated integral curves: a manifestation of chaos. Of special interest are incompressible (with zero divergence) and irrotational (with zero curl) flows. A fixed point of a vector field is a point at which it vanishes. The derivative of a vector field at a fixed point is a matrix (the Jacobi matrix) whose spectrum is independent of the choice of coordinates.

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34

Deruelle, Nathalie, and Jean-Philippe Uzan. Curvilinear coordinates. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0003.

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This chapter presents a discussion on curvilinear coordinates in line with the introduction on Cartesian coordinates in Chapter 1. First, the chapter introduces a new system C of curvilinear coordinates xⁱ = xⁱ(Xj) (also sometimes referred to as Gaussian coordinates), which are nonlinearly related to Cartesian coordinates. It then introduces the components of the covariant derivative, before considering parallel transport in a system of curvilinear coordinates. Next, the chapter shows how connection coefficients of the covariant derivative as well as the Euclidean metric can be related to each other. Finally, this chapter turns to the kinematics of a point particle as well as the divergence and Laplacian of a vector and the Levi-Civita symbol and the volume element.

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35

Chin-Chong, Liew, and Zhou Ying. 9 China. Oxford University Press, 2018. http://dx.doi.org/10.1093/law/9780198808589.003.0009.

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This chapter examines the applicability of the law of set-off in China in cases involving solvent parties and against a party subject to a bankruptcy proceeding. It first explains statutory set-off under the Chinese Contract Law and contractual set-off between solvent parties before discussing set-off against insolvent parties, focusing on the relevant provisions of the Bankruptcy Law and requirements for insolvency set-off. It also considers the procedures for exercising the right to insolvency set-off, set-off right in the context of close-out netting in cross-border over-the-counter (OTC) derivatives transactions, restrictions on unfair preference for creditors and set-off, restrictions on banks' set-off rights against deposits, and set-off vis-a-vis clearing houses. The chapter concludes with an analysis of cross-border issues arising in set-off between solvent parties and against insolvent parties.

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36

Horing, Norman J. Morgenstern. Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0009.

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Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator U(t0+τ,t0). Linear conductivity is exhibited as a two-particle equilibrium Green’s function (Kubo-type formulation). Admitting particle sources (S:η,η+) and non-conservation of number, the non-equilibrium multi-particle Green’s functions are constructed with numbers of creation and annihilation operators that may differ, and they may be derived as variational derivatives with respect to sources η,η+ of a generating functional eW=TrU(t0+τ,t0)CS/TrU(t0+τ,t0)C. (In the non-interacting case this yields the n-particle Green’s function as a permanent/determinant of single-particle Green’s functions.) These variational relations yield a symmetric set of multi-particle Green’s function equations. Cumulants and the Linked Cluster Theorem are discussed and the Random Phase Approximation (RPA) is derived variationally. Schwinger’s variational differential formulation of perturbation theories for the Green’s function, self-energy, vertex operator, and also shielded potential perturbation theory, are reviewed. The Langreth Algebra arises from analytic continuation of integration of products of Green’s functions in imaginary time to the real-time axis with time-ordering along the integration contour in the complex time plane. An account of the Generalized Kadanoff-Baym Ansatz is presented.

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37

Lattman, Eaton E., Thomas D. Grant, and Edward H. Snell. Quantities Directly Measurable by Scattering. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199670871.003.0003.

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In this chapter we note that solution scattering data can be divided into four regions. At zero scattering angle, the scattering provides information on molecular weight of the particle in solution. Beyond that, the scattering is influenced by the radius of gyration. As the scattering angle increases, the scattering is influenced by the particle shape, and finally by the interface with the particle and the solution. There are a number of important invariants that can be calculated directly from the data including molecular mass, radius of gyration, Porod invariant, particle volume, maximum particle dimension, particle surface area, correlation length, and volume of correlation. The meaning of these is described in turn along with their mathematical derivations.

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38

Duffy, Daniel J. Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach. Wiley & Sons, Incorporated, John, 2013.

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39

Duffy, Daniel J. Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach. Wiley & Sons, Incorporated, John, 2007.

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40

Meyer, Gunter H. Time-Discrete Method of Lines for Options and Bonds: A PDE Approach. World Scientific Publishing Co Pte Ltd, 2014.

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41

Pablo, Perezalonso. 21 Mexico. Oxford University Press, 2018. http://dx.doi.org/10.1093/law/9780198808589.003.0021.

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This chapter discusses the law of set-off in Mexico. Under Mexican law, the right of set-off is a form of payment of obligations by which cross-claims may be extinguished up to the amount of the smaller claim. Set-off is not treated as a security interest in Mexico. In order for a set-off to be valid, it is not necessary to satisfy the formal requirements for security interests including executing specific security agreements such as security trusts, pledges, or mortgages. The chapter first considers set-off between solvent parties, focusing on automatic set-off and contractual set-off, before analysing set-off against insolvent parties. In particular, it examines the relevant provisions of the Bankruptcy Law with respect to outstanding obligations resulting from financial derivatives, reportos, and securities lending transactions, along with the retroactivity period for such transactions. Finally, it looks at set-off issues in a cross-border context.

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42

Duffy, Daniel J. Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach (The Wiley Finance Series). Wiley, 2006.

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43

Olivier, Hubert. 14 France. Oxford University Press, 2018. http://dx.doi.org/10.1093/law/9780198808589.003.0014.

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This chapter examines the law of set-off in France and how the country's bankruptcy law may affect the effectiveness of set-off. In France, set-off has been reaffirmed by specific rules regarding the netting of derivative products or by the EU Directive on Financial Collateral Arrangements (Collateral Directive). Other laws with relevant provisions for set-off include the French Civil Code and the French Monetary and Financial Code. The chapter first provides an overview of set-off between solvent parties, focusing on legal set-off, contractual set-off, enhanced set-off of financial obligations, cash-pooling arrangements, and security interests. It then considers set-off against insolvent parties, taking into account issues relating to automatic stay, fraudulent transfers/suspect period, and set-off of financial obligations after opening of an insolvency procedure. It also discusses the key set-off provisions of the Collateral Directive before concluding with an analysis of the law applicable to set-off in a cross-border context.

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44

Booij, Geert. Inheritance and motivation in Construction Morphology. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198712329.003.0002.

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The basic question to be addressed in this chapter is: what is the status of the notions ‘inheritance’ and ‘default inheritance’ in the theoretical framework of Construction Morphology (CM)? This framework, developed in Booij (2010), assumes a hierarchical lexicon with both abstract morphological schemas and stored complex words that instantiate these schemas. The lexicon of a language can be modelled in such a way that the abstract word formation schemas dominate their individual instantiations. Thus, the lexicon is partially conceived of as a hierarchical network in which lower nodes, the existing complex words, can be assumed to inherit information from dominating higher nodes. Advantages of a full-entry theory over an impoverished entry theory are outlined, and the chapter includes discussion of polysemy, allomorphy, and the class of items that fall between derivatives and compounds using ‘affixoids’.

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45

Furst, Eric M., and Todd M. Squires. Light scattering microrheology. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199655205.003.0005.

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The fundamentals and best practices of passive microrheology using dynamic light scattering and diffusing wave spectroscopy are discussed. The principles of light scattering are introduced and applied in both the single and multiple scattering regimes, including derivations of the light and field autocorrelation functions. Applications to high-frequency microrheology and polymer dynamics are presented, including inertial corrections. Methods to treat gels and other non-ergodic samples, including multi-speckle and optical mixing designs are discussed. Dynamic light scattering (DLS) is a well established method for measuring the motion of colloids, proteins and macromolecules. Light scattering has several advantages for microrheology, especially given the availability of commercial instruments, the relatively large sample volumes that average over many probes, and the sensitivity of the measurement to small particle displacements, which can extend the range of length and timescales probed beyond those typically accessed by the methods of multiple particle tracking and bulk rheology.

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46

Canarutto, Daniel. Gauge Field Theory in Natural Geometric Language. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198861492.001.0001.

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This monograph addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a not-too-short, integrated approach that exploits standard and non-standard notions in natural geometric language. The role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. Two-spinors yield a partly original ‘minimal geometric data’ approach to Einstein-Cartan-Maxwell-Dirac fields. The gravitational field is jointly represented by a spinor connection and by a soldering form (a ‘tetrad’) valued in a vector bundle naturally constructed from the assumed 2-spinor bundle. We give a presentation of electroweak theory that dispenses with group-related notions, and we introduce a non-standard, natural extension of it. Also within the 2-spinor approach we present: a non-standard view of gauge freedom; a first-order Lagrangian theory of fields with arbitrary spin; an original treatment of Lie derivatives of spinors and spinor connections. Furthermore we introduce an original formulation of Lagrangian field theories based on covariant differentials, which works in the classical and quantum field theories alike and simplifies calculations. We offer a precise mathematical approach to quantum bundles and quantum fields, including ghosts, BRST symmetry and anti-fields, treating the geometry of quantum bundles and their jet prolongations in terms Frölicher's notion of smoothness. We propose an approach to quantum particle physics based on the notion of detector, and illustrate the basic scattering computations in that context.

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47

Freeman, Richard R., James A. King, and Gregory P. Lafyatis. Electromagnetic Radiation. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198726500.001.0001.

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Electromagnetic Radiation is a graduate level book on classical electrodynamics with a strong emphasis on radiation. This book is meant to quickly and efficiently introduce students to the electromagnetic radiation science essential to a practicing physicist. While a major focus is on light and its interactions, topics in radio frequency radiation, x-rays, and beyond are also treated. Special emphasis is placed on applications, with many exercises and homework problems. The format of the book is designed to convey the basic concepts of a topic in the main central text in the book in a mathematically rigorous manner, but with detailed derivations routinely relegated to the accompanying side notes or end of chapter “Discussions.” The book is composed of four parts: Part I is a review of basic E&M, and assumes the reader has a had a good upper division undergraduate course, and while it offers a concise review of topics covered in such a course, it does not treat any given topic in detail; specifically electro- and magnetostatics. Part II addresses the origins of radiation in terms of time variations of charge and current densities within the source, and presents Jefimenko’s field equations as derived from retarded potentials. Part III introduces special relativity and its deep connection to Maxwell’s equations, together with an introduction to relativistic field theory, as well as the relativistic treatment of radiation from an arbitrarily accelerating charge. A highlight of this part is a chapter on the still partially unresolved problem of radiation reaction on an accelerating charge. Part IV treats the practical problems of electromagnetic radiation interacting with matter, with chapters on energy transport, scattering, diffraction and finally an illuminating, application-oriented treatment of fields in confined environments.

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Books on the topic 'Partial derivatives'

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