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ISBN: 0486654273 Year: 1997 Publisher: Mineola, NY : Dover Publications,
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High-level monograph focuses on an explicit treatment of the principle of general covariance as applied to electromagnetics, examining& among other subjects& the natural invariance of the Maxwell equations, general properties of the medium, nonuniformity, anisotropy and general coordinates in three-space, reciprocity and nonreciprocity, and matter-free space with a gravitational field. Of value to anyone interested in classical physics and to graduate students with a background in electromagnetic theory. 1962 ed.
ISBN: 088385953X 9780883859537 0883856417 9780883856413 Year: 1997 Publisher: Washington : Mathematical Association of America,
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Suitable as supplemental reading in courses in differential and integral calculus, numerical analysis, approximation theory and computer-aided geometric design. Relations of mathematical objects to each other are expressed by transformations. The repeated application of a transformation over and over again, i.e., its iteration leads to solution of equations, as in Newton's method for finding roots, or Picard's method for solving differential equations. This book studies a treasure trove of iterations, in number theory, analysis and geometry, and applied them to various problems, many of them taken from international and national Mathematical Olympiad competitions. Among topics treated are classical and not so classical inequalities, Sharkovskii's theorem, interpolation, Bernstein polynomials, Bzier curves and surfaces, and splines. Most of the book requires only high school mathematics; the last part requires elementary calculus. This book would be an excellent supplement to courses in calculus, differential equations,, numerical analysis, approximation theory and computer-aided geometric design.
ISBN: 9780857099808 0857099809 1898563136 9781898563136 1898563128 9781898563129 Year: 1997 Publisher: Chichester, England : Albion Publishing,
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This text for advanced undergraduates and graduates reading applied mathematics, electrical, mechanical, or control engineering, employs block diagram notation to highlight comparable features of linear differential and difference equations, a unique feature found in no other book. The treatment of transform theory (Laplace transforms and z-transforms) encourages readers to think in terms of transfer functions, i.e. algebra rather than calculus. This contrives short-cuts whereby steady-state and transient solutions are determined from simple operations on the transfer functions.
Economics --- Didactic evaluation --- Differential equations, Linear. --- Difference equations. --- System analysis. --- Transformations (Mathematics) --- Great Britain --- Economic policy
ISBN: 1139882309 1107103304 1107088976 1107100836 1107095182 1139086545 9781107088979 0521573521 9780521573528 9781139086547 9780521057189 Year: 1997 Volume: v. 66 Publisher: Cambridge : Cambridge University Press,
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Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research.
Graph theory. --- Spectral theory (Mathematics) --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Extremal problems
ISSN: 00659266 ISBN: 0821805975 Year: 1997 Publisher: Providence (R.I.): American Mathematical Society
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Differential equations --- Differential equations, Partial --- Équations aux dérivées partielles --- Spectral theory (Mathematics) --- Théorie spectrale (mathématiques) --- Functions, Zeta. --- Fonctions zêta. --- Fractals. --- Fractales. --- Numerical solutions. --- Solutions numériques. --- Fractals --- Functions, Zeta --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Zeta functions --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Numerical analysis --- Numerical solutions --- Solutions numériques
ISBN: 0521592097 0521597714 9780521592093 9780521597715 Year: 1997 Publisher: Cambridge Cambridge University press
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The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms and Laplace transforms. The book is an expanded and polished version of the authors' notes for a one semester course, for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. Otherwise the material is self-contained with numerous exercises and various examples of applications.
Fourier series --- Integral transforms. --- 517.518.4 --- 517.518.5 --- Integral transforms --- #KVIV:BB --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Harmonic analysis --- Harmonic functions --- Theory of the Fourier integral --- Fourier series. --- 517.518.5 Theory of the Fourier integral --- 517.518.4 Trigonometric series
ISBN: 0857099809 1898563128 9780857099808 1898563136 9781898563136 9781898563129 Year: 1997 Publisher: Oxford Woodhead
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This text for advanced undergraduates and graduates reading applied mathematics, electrical, mechanical, or control engineering, employs block diagram notation to highlight comparable features of linear differential and difference equations, a unique feature found in no other book. The treatment of transform theory (Laplace transforms and z-transforms) encourages readers to think in terms of transfer functions, i.e. algebra rather than calculus. This contrives short-cuts whereby steady-state and transient solutions are determined from simple operations on the transfer functions.
Differential equations, Linear. --- Difference equations. --- System analysis. --- Transformations (Mathematics) --- Algorithms --- Differential invariants --- Geometry, Differential --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Linear differential equations --- Linear systems --- 517.95 --- 517.95 Partial differential equations --- Partial differential equations --- Great Britain --- Economic policy
ISBN: 3540627316 3540684964 9783540627319 Year: 1997 Volume: 1658 Publisher: Berlin ; Heidelberg ; New York Springer Verlag
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Differential geometry. Global analysis --- Chaotic behavior in systems. --- Chaotic behavior in systems --- Mathematical Theory --- Sciences - General --- Mathematics --- Physical Sciences & Mathematics --- Chaos in systems --- Chaotic motion in systems --- Chaotisch gedrag in de systemen --- Comportement chaotique dans les systèmes --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Dynamics. --- Ergodic theory. --- Global Analysis and Analysis on Manifolds. --- Dynamical Systems and Ergodic Theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Chaos theory --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory
ISBN: 0817636951 1461266920 1461202817 Year: 1997 Publisher: Boston Birkhäuser
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This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization. The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. The first tow chapters provide the necessary mathematical background in differential geometry, Lie groups, and symplectic geometry. In Chapter 3 a coherent symplectic description of Galilean and relativistic mechanics is given, culminating in the classification of elementary particles (relativistic and non-relativistic, with or without spin, with or without mass). In Chapter 4 statistical mechanics is put into symplectic form, finishing with a symplectic description of the kinetic theory of gases and the computation of specific heats. Finally, in Chapter 5 the author presents his theory of geometric quantization. Highlights of this chapter are the derivations of various wave equations and the construction of the Fock space.
Differential geometry. Global analysis --- Mathematical physics. --- Mechanics. --- Quantum theory. --- Statistical mechanics. --- Symplectic manifolds. --- Differential geometry. --- Dynamics. --- Ergodic theory. --- Manifolds (Mathematics). --- Complex manifolds. --- Differential Geometry. --- Dynamical Systems and Ergodic Theory. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Differential geometry --- Physical mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Thermodynamics --- Quantum statistics --- Statistical physics --- Manifolds, Symplectic
ISBN: 089871382X 9780898713824 Year: 1997 Publisher: Philadelphia, PA : Society for Industrial & Applied Mathematics,
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Linear Programming --- Mathematical optimization --- 519.8 --- Linear programming --- Interior-point methods --- #TELE:SISTA --- 681.3*G16 --- Programming (Mathematics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Matrices --- Production scheduling --- Substitutions, Linear --- Transformations (Mathematics) --- Vector analysis --- Operational research --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 519.8 Operational research --- Linear programming. --- Programmation (mathématiques) --- Programmation mathematique --- Programmation lineaire
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