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1.

図書

図書
Kurt Lechner
出版情報: [Cham] : Springer, c2018  xix, 688 p. ; 25 cm
シリーズ名: Unitext for physics
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2.

図書

図書
edited by S.M. Blinder, J.E. House
出版情報: Amsterdam : Elsevier, c2019  xv, 408 p. ; 24 cm
シリーズ名: Developments in physical & theoretical chemistry
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3.

図書

図書
Oleg V. Petrov
出版情報: Cham : Springer, c2019  xv, 270 p. ; 25 cm
シリーズ名: Springer geophysics
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4.

図書

図書
von K.P. Jakowlew ; [Übersetzung aus dem Russischen, Hans Rudel]
出版情報: Berlin : Technik, 1952  262 p. ; 24 cm
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5.

図書

図書
M. Göckeler, T. Schücker
出版情報: Cambridge ; New York : Cambridge University Press, 1989  xii, 230 p. ; 23 cm
シリーズ名: Cambridge monographs on mathematical physics
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目次情報: 続きを見る
Preface
Exterior algebra / 1:
Differential forms on open subsets of Rn / 2:
Metric structures / 3:
Gauge theories / 4:
Einstein-Cartan theory / 5:
The Lie derivative / 6:
Manifolds / 7:
Lie groups / 8:
Fibre bundles / 9:
Monopoles, instantons, and related fibre bundles / 10:
Spin / 11:
An algebraic approach to anomalies / 12:
Anomalies from graphs / 13:
References
Bibliography
Notation
Index
Preface
Exterior algebra / 1:
Differential forms on open subsets of Rn / 2:
6.

図書

図書
G.I. Barenblatt ; translated from Russian by Norman Stein ; translation editor, Milton van Dyke
出版情報: New York : Consultants Bureau, c1979  xvii, 218 p. ; 24 cm
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7.

図書

図書
Edited by George A. Baker, Jr. and John L. Gammel
出版情報: New York : Academic Press, 1970  xii, 378 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 71
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8.

図書

図書
by F.J. Belinfante
出版情報: Oxford : Pergamon Press, 1973  xix, 354 p. ; 25 cm
シリーズ名: International series of monographs in natural philosophy ; v. 55
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9.

図書

図書
edited by M. Sh. Birman ; translated from Russian by J.R. Schulenberger
出版情報: New York : Consultants Bureau, 1971  v, 121 p. ; 28 cm
シリーズ名: Topics in mathematical physics ; v. 4
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10.

図書

図書
edited by Wesley E. Brittin
出版情報: Boulder : Colorado Associated University Press, c1973  x, 568 p ; 24 cm
シリーズ名: Lectures in theoretical physics / edited by Wesley E. Brittin and Lita G. Dunham ; v. 14B
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11.

図書

図書
editors, P.H. Damgaard and H. Hüffel
出版情報: Singapore : World Scientific, c1988  xii, 496 p. ; 26 cm
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12.

図書

図書
Ronald B. Guenther and John W. Lee
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1988  xii, 544 p. ; 25 cm
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13.

図書

図書
Siegfried Flügge
出版情報: Berlin ; New York : Springer-Verlag, 1971  2 v. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 177-178
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14.

図書

図書
Charles Nash, Siddhartha Sen
出版情報: London ; Tokyo : Academic Press, 1983  x, 311 p. ; 24 cm
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目次情報: 続きを見る
Preface
Basic Notions of Topology and the Value of Topological Reasoning
Differential Geometry
Manifolds and Differential Forms
The Fundamental Group
The Homology Groups
The Higher Homotopy Groups
Cohomology and De Rham Cohomology
Fibre Bundles and Further Differential Geometry
Morse Theory
Defects, Textures, and Homotopy Theory
Yang-Mills Theories
Instantons and Monopoles
Subject Index
Preface
Basic Notions of Topology and the Value of Topological Reasoning
Differential Geometry
15.

図書

図書
Yvonne Choquet-Bruhat, Cécile DeWitt-Morette, and Margaret Dillard-Bleick
出版情報: Amsterdam ; New York : North Holland Pub., 1977  xvii, 544 p. ; 25 cm
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目次情報: 続きを見る
Preface
Preface to the second edition
Contents
Conventions
Review of fundamental notions of analysis / I:
Differential calculus on banach spaces / II:
Differentiable manifolds / III:
Integration on manifolds / IV:
Riemannian manifolds, Kahlerian manifolds / V:
bis. Connections on a principle fibre bundle
Distributions / VI:
Supplements and additional problems
Subject Index
Errata to Part I
Preface
Preface to the second edition
Contents
16.

図書

図書
[by] N.N. Lebedev ; translated and edited by Richard A. Silverman
出版情報: New York : Dover Publications, 1972  xii, 308 p. ; 22 cm
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17.

図書

図書
Robert D. Richtmyer
出版情報: New York ; Tokyo : Springer Verlag, c1978-1981  2 v. ; 25 cm
シリーズ名: Texts and monographs in physics
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18.

図書

図書
Louis A. Pipes, Lawrence R. Harvill
出版情報: New York ; Tokyo : McGraw-Hill, c1971  xxii, 1015 p. ; 23 cm
シリーズ名: International series in pure and applied mathematics
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19.

図書

図書
Victor Guillemin, Shlomo Sternberg
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984  xi, 468 p. ; 24 cm
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目次情報: 続きを見る
Preface
Introduction / I:
Gaussian optics / 1:
Hamilton's method in Gaussian optics / 2:
Fermat's principle / 3:
From Gaussian optics to linear optics / 4:
Geometrical optics, Hamilton's method, and the theory of geometrical aberrations / 5:
Fermat's principle and Hamilton's principle / 6:
Interference and diffraction / 7:
Gaussian integrals / 8:
Examples in Fresnel optics / 9:
The phase factor / 10:
Fresnel's formula / 11:
Fresnel optics and quantum mechanics / 12:
Holography / 13:
Poisson brackets / 14:
The Heisenberg group and representation / 15:
The Groenwald-van Hove theorem / 16:
Other quantizations / 17:
Polarization of light / 18:
The coadjoint orbit of a semidirect product / 19:
Electromagnetism and the determination of symplectic structures / 20:
Epilogue: Why symplectic geometry?
The geometry of the moment map / II:
Normal forms / 21:
The Darboux-Weinstein theorem / 22:
Kaehler manifolds / 23:
Left-invariant forms and Lie algebra cohomology / 24:
Symplectic group actions / 25:
The moment map and some of its properties / 26:
Group actions and foliations / 27:
Collective motion / 28:
Cotangent bundles and the moment map for semidirect products / 29:
More Euler-Poisson equations / 30:
The choice of a collective Hamiltonian / 31:
Convexity properties of toral group actions / 32:
The lemma of stationary phase / 33:
Geometric quantization / 34:
Motion in a Yang-Mills field and the principle of general covariance / III:
The equations of motion of a classical particle in a Yang-Mills field / 35:
Curvature / 36:
The energy-momentum tensor and the current / 37:
The principle of general covariance / 38:
Isotropic and coisotropic embeddings / 39:
Symplectic induction / 40:
Symplectic slices and moment reconstruction / 41:
An alternative approach to the equations of motion / 42:
The moment map and kinetic theory / 43:
Complete integrability / IV:
Fibrations by tori / 44:
Collective complete integrability / 45:
Collective action variables / 46:
The Kostant-Symes lemma and some of its variants / 47:
Systems of Calogero type / 48:
Solitons and coadjoint structures / 49:
The algebra of formal pseudodifferential operators / 50:
The higher-order calculus of variations in one variable / 51:
Contractions of symplectic homogeneous spaces / V:
The Whitehead lemmas / 52:
The Hochschild-Serre spectral sequence / 53:
Galilean and Poincare elementary particles / 54:
Coppersmith's theory / 55:
References
Index
Preface
Introduction / I:
Gaussian optics / 1:
20.

図書

図書
by Arnold Sommerfeld ; translated by Edward G. Ramberg
出版情報: New York : Academic Press, 1952  xiii, 371 p. ; 24 cm
シリーズ名: Lectures on theoretical physics ; vol. 3
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21.

図書

図書
by Arnold Sommerfeld ; translated by Otto Laporte and Peter A. Moldauer
出版情報: New York : Academic Press, 1954  xii, 383 p. ; 24 cm
シリーズ名: Lectures on theoretical physics ; 4
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22.

図書

図書
by Eugene R. Speer
出版情報: Princeton, N.J. : Princeton University Press , [Tokyo] : University of Tokyo Press, 1969  120 p. ; 24 cm
シリーズ名: Annals of mathematics studies ; no. 62
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23.

図書

図書
Andrzej Trautman
出版情報: Napoli : Bibliopolis, c1984  145 p. ; 23 cm
シリーズ名: Monographs and textbooks in physical science ; 2
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24.

図書

図書
Jamal Nazrul Islam
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1985  vi, 122 p. ; 24 cm
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目次情報: 続きを見る
Preface
Introduction / 1:
The Einstein equations for a rotating metric and some classes of solutions / 2:
The Kerr and Timimatsu-Sato solutions / 3:
Rotating neutral dust / 4:
rotating Einstein-Maxwell fields / 5:
Rotating charged dust / 6:
Appendix
References
Index
Preface
Introduction / 1:
The Einstein equations for a rotating metric and some classes of solutions / 2:
25.

図書

図書
Bryce DeWitt
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984  xiv, 316 p. ; 24 cm
シリーズ名: Cambridge monographs on mathematical physics
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目次情報: 続きを見る
Preface to the first edition
Preface to the second edition
Analysis over supernumbers / 1:
Supernumbers and superanalytic functions / 1.1:
Grassmann algebras
Supernumbers
c-numbers and a-numbers
Superanalytic functions of supernumbers
Integration of superanalytic functions of supernumbers
Real supernumbers. Differentiable functions of real c-numbers and their integrals / 1.2:
Complex conjugation
Functions, distributions and integrals over R[subscript c]
Fourier transforms over R[subscript c]
Functions and integrals over R[subscript a] / 1.3:
Basic definitions
Fourier transforms over R[subscript a]
Integrals over R[superscript n][subscript a]
Supervector spaces / 1.4:
Definition
Bases
Pure bases
Pure real bases
Standard bases
Linear transformations, supertranspositions and dual supervector spaces / 1.5:
Change of basis
Shifting indices. The supertranspose
Extensions of the supertransposition rules
Dual supervector spaces
Dual bases
Further index-shifting conventions
The supertrace and the superdeterminant / 1.6:
The supertrace
The superdeterminant
The superdeterminant in special cases
The superdeterminant in the general case
Integration over R[superscript m][subscript c] [times] R[superscript n][subscript a] / 1.7:
Notation
Integration
Homogeneous linear transformations of the a-number coordinates
Homogeneous linear transformations of all the coordinates
Nonlinear transformations
Gaussian integrals over R[superscript m][subscript c] [times] R[superscript n][subscript a]
Exercises
Comments on chapter 1
Supermanifolds / 2:
Definition and structure of supermanifolds / 2.1:
Topology of R[superscript m][subscript c] [times] R[superscript n][subscript a]. Differentiable mappings
Supermanifolds, charts and atlases
Scalar fields and supercurves
Diffeomorphisms and embeddings
Ordinary manifolds. Skeleton and body of a supermanifold
Projectively Hausdorff, compact, paracompact and orientable supermanifolds. Realizations of the body
Supervector structures on supermanifolds / 2.2:
Scalar fields as supervectors
Contravariant vector fields
Alternative presentation of contravariant vector fields
Components
Tangent spaces
Tangents to supercurves
Super Lie brackets, local frames and covariant vector fields / 2.3:
Supercommutators and antisupercommutators
A matter of notation
The super Lie bracket
Local frames
Super Lie brackets of local frame fields
Covariant vector fields
Differentials
Tensor fields / 2.4:
Tensors at a point
The supervector space T[superscript r] [subscript s](p)
Tensor products
Tensor and multitensor fields
Index-shifting conventions. Contractions
The unit tensor field
The Lie derivative / 2.5:
Explicit forms
Lie derivations as supervectors
The derivative mapping
Integral supercurves. Congruences
Dragging of tensor fields
Forms / 2.6:
The exterior product
Bases for forms
Derivations of forms
The exterior derivative
The inner product
Connections / 2.7:
The connection components
Multiple covariant derivatives. The torsion
The Riemann tensor field
The super Bianchi identity
Parallel transport. Supergeodesics
Distant parallelism
Riemannian supermanifolds / 2.8:
The metric tensor field
Canonical form of the metric tensor at a point
Canonical or orthosymplectic bases
Riemannian connections
The curvature tensor field
The Ricci tensor field
Flat Riemannian supermanifolds
Conformally related Riemannian supermanifolds. The Weyl tensor field
Conformally flat Riemannian supermanifolds
Killing vector fields
Conformal Killing vector fields
The global conformal group
Integration over supermanifolds / 2.9:
Integration over R[superscript m][subscript c] [times] R[superscript n][subscript a]. Measure functions
Locally finite atlases and partitions of unity
Integration over paracompact orientable supermanifolds
Integration over Riemannian supermanifolds
Integrals of total divergences
The compact case
An example
Comments on chapter 2
Super Lie groups. General theory / 3:
Definition and structure of super Lie groups / 3.1:
Canonical diffeomorphisms
Left- and right-invariant vector fields
Left- and right-invariant local frame fields
Left- and right-invariant congruences
One-parameter Abelian subgroups
The exponential mapping. Canonical coordinates
The super Lie algebra
The structure constants
The right and left auxiliary functions
Identities satisfied by the auxiliary functions
Construction of a super Lie group from its super Lie algebra
Realizations of super Lie groups / 3.2:
Orbits
Transitive realizations
Isotropy subgroups
Coset spaces
Killing flows
Properties of the coordinate components of the Q[subscript a]
A special canonical coordinate system
Coordinates for the coset spaces
Classification of transitive realizations
Matrix representations of super Lie groups
Contragredient representations
Inner automorphisms. The adjoint representation
Matrix representations of the super Lie algebra
Geometry of coset spaces / 3.3:
Invariant tensor fields
Differential equations for geometrical structures
Integrability of the differential equations
A special coordinate system
Condition for the existence of a group-invariant measure function
Condition for the existence of a group-invariant metric tensor field
Condition for the existence of a group-invariant connection
Solutions of the differential equations
Geometry of the group supermanifold
Identity of the left- and right-invariant connections
Parallelism at a distance in the group supermanifold
Integration over the group
A special class of super Lie groups
Comments on chapter 3
Super Lie groups. Examples / 4:
Construction of super Lie algebras and super Lie groups / 4.1:
Properties of the structure constants
Conventional super Lie groups, Z[subscript 2]-graded algebras
Unconventional super Lie groups
Structure of conventional super Lie Groups. The extending representation
Construction of a class of super Lie algebras
The classical super Lie groups / 4.2:
The group GL (m, n)
The group SL (m, n)
The group SL (m, m)/GL (1, 0)
The orthosymplectic group OSp (m, n)
The Kac notation
The group P(m)
The group Q(m)
The exceptional simple super Lie groups / 4.3:
The groups D(2, 1, [alpha])
The group F(4)
The structure of F(4)
Pseudorepresentation of F(4)
The group G(3)
The structure of G[subscript 2]
The structure of G(3)
Pseudorepresentation of G(3)
Super Lie groups of basic importance in physics / 4.4:
The super de Sitter group
The super Poincare group
The coset space: super Poincare group/SO(1, 3)
Killing flows and invariant connections
Riemannian geometry of the coset space
The super Lorentz group
The Cartan super Lie groups / 4.5:
The diffeomorphism group Diff(M)
The group SDiff(M, [mu])
The canonical transformation group Can(M, [omega])
The group of contact transformations
The case m = 0
The group W(n)
The groups S(n) and S(n)
The groups H(n) and H(n)
Comments on chapter 4
Selected applications of supermanifold theory / 5:
Superclassical dynamical systems / 5.1:
Configuration spaces
Supermanifolds as configuration spaces
Space of histories
The action functional and the dynamical equations
Infinitesimal disturbances and Green's functions
Reciprocity relations
The Peierls bracket
Peierls bracket identities
Super Hilbert spaces / 5.2:
Linear operators
Physical observables
Quantum systems / 5.3:
Transition to the quantum theory
The Schwinger variational principle
External sources
Chronologically ordered form of the operator dynamical equations
The Feynman functional integral
A simple Fermi system / 5.4:
Action functional and Green's functions
Eigenvectors of x
The energy
A pure basis
An alternative representation
The functional integral representation of [x", t"|x', t']
Evaluation of the functional integral
The average superclassical trajectory
Propagator for x[subscript av](t)
The Fermi oscillator / 5.5:
Mode functions and Hamiltonian
Basic supervectors
Eigenvectors of x[subscript 1] and x[subscript 2]. Choice of pure basis
Coherent states
The functional integral representation of [a"*, t"
Direct evaluation of the functional integral
The importance of endpoint contributions
The stationary trajectory as a matrix element
The Feynman propagator
The Bose oscillator / 5.6:
Energy eigenvectors
Hamilton-Jacobi theory
The amplitude [x', t'|x', t'] and its functional integral representation
The functional-integral representation of [a"*, t"
The stationary path between coherent states
Energy eigenfunctions
Bose-Fermi supersymmetry / 5.7:
The simplest model
New conserved quantities
The Bose-Fermi supersymmetry group
Eigenvectors of Q[subscript 1] and Q[subscript 2]
The supersymmetry group as a transformation group
Auxiliary variable
Nonlinear Bose-Fermi supersymmetry
The supersymmetry group
The energy spectrum
Spontaneously broken supersymmetry
Comments on chapter 5
Applications involving topology / 6:
Nontrivial configuration spaces / 6.1:
Standard canonical systems
Green's functions
Equivalence of Peierls and Poisson brackets
Quantization / 6.2:
Problems with the naive quantization rule
Operator-valued forms. The projection m-form
The position operator
Vector operators
The momentum operator
Restriction to a local chart
Lack of uniqueness of the momentum operator
Overlapping charts. Transformation of coordinates
The position representation
The momentum operator in the position representation
The Schrodinger equation
The position representation of the projection m-form
Curved configuration spaces / 6.3:
A special class of systems
Covariant variation
Covariant differentiation with respect to t
The dynamical equations
Covariant functional differentiation
The Feynman functional integral and its meaning / 6.4:
Formal computation of det G[superscript +][x]
The functional integral
Normalization
Ambiguity in the functional integral
Homotopy
Homotopy mesh
The total amplitude
Change of homotopy mesh
The role of homology
The universal covering space
The total amplitude revisited
The Hamiltonian operator: a nonlattice derivation / 6.5:
Integration over phase space
Evaluation of the chronologically ordered Hamiltonian
Approximate evaluation of the path integral / 6.6:
Brief review of Hamilton-Jacobi theory
The Van Vleck-Morette determinant
Jacobi fields and the Green's function for the trajectory x[subscript c]
Determinantal relations
The loop expansion
The WKB approximation
The heat kernel expansion
Role of the two-loop term in the independent verification of (6.5.25)
New variables
Computation of the two-loop term
Supersymmetry and the Euler-Poincare characteristic / 6.7:
Inclusion of a-type dynamical variables
Green's functions and Peierls brackets
Energy and supersymmetry group
Basis supervectors
Differential representation of operators
The Euler-Poincare characteristic
Functional integral for the coherent-state transition amplitude
The Chern-Gauss-Bonnet formula
Comments on chapter 6
References
Index
Preface to the first edition
Preface to the second edition
Analysis over supernumbers / 1:
26.

図書

図書
by Claude E. Shannon and Warren Weaver
出版情報: Urbana : University of Illinois Press, 1949  v [i.e. vii], 117 p. ; 24 cm
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目次情報:
The mathematical theory of communication / by C.E. Shannon
Recent contributions to the mathematical theory of communication / by W. Weaver
The mathematical theory of communication / by C.E. Shannon
Recent contributions to the mathematical theory of communication / by W. Weaver
27.

図書

図書
George Papanicolaou, editor
出版情報: New York ; Tokyo : Springer-Verlag, c1987  xi, 321 p. ; 25 cm
シリーズ名: The IMA volumes in mathematics and its applications ; v. 7
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28.

図書

図書
W.I. Fushchich and A.G. Nikitin ; translated by John R. Schulenberger
出版情報: Dordrecht [Netherlands] ; Tokyo : D. Reidel, c1987  xiv, 214 p. ; 25 cm
シリーズ名: Mathematics and its applications ; Soviet series
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29.

図書

図書
Donald Greenspan
出版情報: New York : Academic Press, 1974  xi, 312 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 107
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30.

図書

図書
Bernard F. Schutz
出版情報: Cambridge ; New York : Cambridge University Press, 1980  xii, 250 p. ; 24 cm
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目次情報: 続きを見る
Preface
Some basic mathematics / 1:
The space R[superscript n] and its topology / 1.1:
Mappings / 1.2:
Real analysis / 1.3:
Group theory / 1.4:
Linear algebra / 1.5:
The algebra of square matrices / 1.6:
Bibliography / 1.7:
Differentiable manifolds and tensors / 2:
Definition of a manifold / 2.1:
The sphere as a manifold / 2.2:
Other examples of manifolds / 2.3:
Global considerations / 2.4:
Curves / 2.5:
Functions on M / 2.6:
Vectors and vector fields / 2.7:
Basis vectors and basis vector fields / 2.8:
Fiber bundles / 2.9:
Examples of fiber bundles / 2.10:
A deeper look at fiber bundles / 2.11:
Vector fields and integral curves / 2.12:
Exponentiation of the operator d/d[lambda] / 2.13:
Lie brackets and noncoordinate bases / 2.14:
When is a basis a coordinate basis? / 2.15:
One-forms / 2.16:
Examples of one-forms / 2.17:
The Dirac delta function / 2.18:
The gradient and the pictorial representation of a one-form / 2.19:
Basis one-forms and components of one-forms / 2.20:
Index notation / 2.21:
Tensors and tensor fields / 2.22:
Examples of tensors / 2.23:
Components of tensors and the outer product / 2.24:
Contraction / 2.25:
Basis transformations / 2.26:
Tensor operations on components / 2.27:
Functions and scalars / 2.28:
The metric tensor on a vector space / 2.29:
The metric tensor field on a manifold / 2.30:
Special relativity / 2.31:
Lie derivatives and Lie groups / 2.32:
Introduction: how a vector field maps a manifold into itself / 3.1:
Lie dragging a function / 3.2:
Lie dragging a vector field / 3.3:
Lie derivatives / 3.4:
Lie derivative of a one-form / 3.5:
Submanifolds / 3.6:
Frobenius' theorem (vector field version) / 3.7:
Proof of Frobenius' theorem / 3.8:
An example: the generators of S[superscript 2] / 3.9:
Invariance / 3.10:
Killing vector fields / 3.11:
Killing vectors and conserved quantities in particle dynamics / 3.12:
Axial symmetry / 3.13:
Abstract Lie groups / 3.14:
Examples of Lie groups / 3.15:
Lie algebras and their groups / 3.16:
Realizations and representations / 3.17:
Spherical symmetry, spherical harmonics and representations of the rotation group / 3.18:
Differential forms / 3.19:
The algebra and integral calculus of forms / A:
Definition of volume -- the geometrical role of differential forms / 4.1:
Notation and definitions for antisy mmetric tensors / 4.2:
Manipulating differential forms / 4.3:
Restriction of forms / 4.5:
Fields of forms / 4.6:
Handedness and orientability / 4.7:
Volumes and integration on oriented manifolds / 4.8:
N-vectors, duals, and the symbol [epsilon][subscript ij...k] / 4.9:
Tensor densities / 4.10:
Generalized Kronecker deltas / 4.11:
Determinants and [epsilon][subscript ij...k] / 4.12:
Metric volume elements / 4.13:
The differential calculus of forms and its applications / B:
The exterior derivative / 4.14:
Notation for derivatives / 4.15:
Familiar examples of exterior differentiation / 4.16:
Integrability conditions for partial differential equations / 4.17:
Exact forms / 4.18:
Proof of the local exactness of closed forms / 4.19:
Lie derivatives of forms / 4.20:
Lie derivatives and exterior derivatives commute / 4.21:
Stokes' theorem / 4.22:
Gauss' theorem and the definition of divergence / 4.23:
A glance at cohomology theory / 4.24:
Differential forms and differential equations / 4.25:
Frobenius' theorem (differential forms version) / 4.26:
Proof of the equivalence of the two versions of Frobenius' theorem / 4.27:
Conservation laws / 4.28:
Vector spherical harmonics / 4.29:
Applications in physics / 4.30:
Thermodynamics
Simple systems / 5.1:
Maxwell and other mathematical identities / 5.2:
Composite thermodynamic systems: Caratheodory's theorem / 5.3:
Hamiltonian mechanics
Hamiltonian vector fields / 5.4:
Canonical transformations / 5.5:
Map between vectors and one-forms provided by [characters not reproducible] / 5.6:
Poisson bracket / 5.7:
Many-particle systems: symplectic forms / 5.8:
Linear dynamical systems: the symplectic inner product and conserved quantities / 5.9:
Fiber bundle structure of the Hamiltonian equations / 5.10:
Electromagnetism / C:
Rewriting Maxwell's equations using differential forms / 5.11:
Charge and topology / 5.12:
The vector potential / 5.13:
Plane waves: a simple example / 5.14:
Dynamics of a perfect fluid / D:
Role of Lie derivatives / 5.15:
The comoving time-derivative / 5.16:
Equation of motion / 5.17:
Conservation of vorticity / 5.18:
Cosmology / E:
The cosmological principle / 5.19:
Lie algebra of maximal symmetry / 5.20:
The metric of a spherically symmetric three-space / 5.21:
Construction of the six Killing vectors / 5.22:
Open, closed, and flat universes / 5.23:
Connections for Riemannian manifolds and gauge theories / 5.24:
Introduction / 6.1:
Parallelism on curved surfaces / 6.2:
The covariant derivative / 6.3:
Components: covariant derivatives of the basis / 6.4:
Torsion / 6.5:
Geodesics / 6.6:
Normal coordinates / 6.7:
Riemann tensor / 6.8:
Geometric interpretation of the Riemann tensor / 6.9:
Flat spaces / 6.10:
Compatibility of the connection with volume-measure or the metric / 6.11:
Metric connections / 6.12:
The affine connection and the equivalence principle / 6.13:
Connections and gauge theories: the example of electromagnetism / 6.14:
Solutions and hints for selected exercises / 6.15:
Notation
Index
Appendix
Preface
Some basic mathematics / 1:
The space R[superscript n] and its topology / 1.1:
31.

図書

図書
Reginald J. Stephenson
出版情報: New York : Wiley , Tokyo : Toppan, c1969  xiii, 375 p. ; 22 cm
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32.

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図書
edited by Donald H. Menzel
出版情報: New York : Dover Publications, 1960  2 v. (xx, 741 p.) ; 21 cm
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33.

図書

図書
Walter Thirring ; translated by Evans M. Harrell
出版情報: New York : Springer, c1981  viii, 300 p. ; 25 cm
シリーズ名: A course in mathematical physics / Walter Thirring ; 3
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34.

図書

図書
Robert Carroll
出版情報: Amsterdam ; Tokyo : North-Holland, 1988  x, 399 p. ; 25 cm
シリーズ名: North-Holland mathematics studies ; 152
Notas de matemática ; 121
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35.

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図書
Gregory L. Naber
出版情報: New York : Springer, c2000  xiii, 443 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; 141
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Preface
Acknowledgements
Geometrical Background
Physical Motivation
Frame Bundles and Spacetime
Differential Forms and Integration Introduction
de Rham Cohomology Introduction
Characteristic Classes
Appendix
References
Symbols
Index
Preface
Acknowledgements
Geometrical Background
36.

図書

図書
Aleksey I. Prilepko, Dmitry G. Orlovsky, Igor A. Vasin
出版情報: New York : Marcel Dekker, c2000  xiii, 709 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 231
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Inverse problems for equations of parabolic type
inverse problems for equations of hyperbolic type
inverse problems for equations of elliptic type
inverse problems in dynamics of viscous incompressible fluid
some topics from functional analysis and operator theory
abstract inverse problems for first order equations and their applications in mathematical physics
two-point inverse problems for first order equations
inverse problems for equations of second order
applications of
Inverse problems for equations of parabolic type
inverse problems for equations of hyperbolic type
inverse problems for equations of elliptic type
37.

図書

図書
Ioannis P. Stavroulakis, Stepan A. Tersian
出版情報: Singapore ; River Edge, N.J. : World Scientific, c1999  x, 297 p. ; 23 cm
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First-order Partial Differential Equations / 1.:
Introduction
Linear First-order Equations / 2.:
The Cauchy Problem for First-order Quasi-linear Equations / 3.:
General Solutions of Quasi-linear Equations / 4.:
Fully-nonlinear First-order Equations / 5.:
Second-order Partial Differential Equations
Linear equations / 6.:
Classification and Canonical Forms of Equations in Two Independent Variables / 7.:
Classification of Almost-linear Equations in R[superscript n] / 8.:
One-Dimensional Wave Equation
The Wave Equation on the Whole Line. D'Alembert Formula / 9.:
The Wave Equation on the Half-line. Reflection Method / 10.:
Mixed Problem for the Wave Equation / 11.:
Inhomogeneous Wave Equation / 12.:
Conservation of the Energy / 13.:
Weak Derivatives and Weak Solutions / 14.:
One-Dimensional Diffusion Equation
Maximum-minimum Principle for the Diffusion Equation / 15.:
The Diffusion Equation on the Whole Line / 16.:
Diffusion on the Half-line / 17.:
Inhomogeneous Diffusion Equation on the Whole Line / 18.:
Shock Waves and Conservation Laws
Conservation laws / 19.:
Burgers' Equation / 20.:
Weak Solutions. Riemann Problem / 21.:
Discontinuous Solutions of Conservation Laws. Rankine-Hugoniot Condition / 22.:
The Laplace Equation
Harmonic functions. Maximum-minimum Principle / 23.:
Green's Identities / 24.:
Green's Functions / 25.:
Green's Functions for a Half-space and Sphere / 26.:
Harnack's Inequalities and Theorems / 27.:
Fourier Series and Fourier Method for PDEs
Fourier Series / 28.:
Orthonormal Systems. General Fourier series / 29.:
Fourier Method for the Diffusion Equation / 30.:
Fourier Method for the Wave Equation / 31.:
Fourier Method for the Laplace Equation / 32.:
Diffusion and Wave Equations in Higher Dimensions
Diffusion Equation in Three Dimensional Space / 33.:
Fourier Method for the Diffusion Equation in Higher Dimensions / 34.:
Kirchoff's Formula for the Wave Equation. Huygens' Principle / 35.:
Fourier Method for the Wave Equation on the Plane. Nodal Sets / 36.:
References
Answers and Hints to Selected Exercises
Index
First-order Partial Differential Equations / 1.:
Introduction
Linear First-order Equations / 2.:
38.

図書

図書
James J. Callahan
出版情報: New York : Springer, c2000  xvi, 451 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
Arbitrary frames
Surfaces and curvatures
Intrinsic geometry
General relativity
Consequences
Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
39.

図書

図書
L. Ambrosio, N. Dancer ; edited by G. Buttazzo, A. Marino, M.K.V. Murthy
出版情報: Berlin : Springer, c2000  viii, 347 p. ; 24 cm
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40.

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図書
by Zbigniew Haba
出版情報: Dordrecht : Kluwer Academic Publishers, c1999  xx, 364 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 480
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41.

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図書
Michael Monastyrsky ; with a foreword by Freeman J. Dyson ; translated by Roger Cooke, James King, Victoria King
出版情報: Boston : Birkhäuser, c1999  xiii, 215 p. ; 25 cm
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42.

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図書
edited by Alexander I. Bobenko and Ruedi Seiler
出版情報: New York : Oxford University Press, 1999  xxvii, 370 p. ; 25 cm
シリーズ名: Oxford lecture series in mathematics and its applications ; 16
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List of contributors
Introduction / Alexander I. Bobenko ; Ruedi Seiler
Geometry / I:
Discretization of Surfaces and Integrable Systems / Ulrich Pinkall1:
A Discrete Version of the Darboux Transform for Isothermic Surfaces / Udo Hertrich-Jeromin ; Tim Hoffmann2:
Discrete Amsler Surfaces and a Discrete Painleve III Equation / 3:
Discrete cmc Surfaces and Discrete Holomorphic Maps / 4:
Discrete Indefinite Affine Spheres / Wolfgang K. Schief5:
Geometry of Discrete Curves and Lattices and Integrable Difference Equations / Adam Doliwa ; Paolo Maria Santini6:
Classical Systems / II:
R-matrices and Integrable Discretizations / Yuri B. Suris7:
Discrete Painleve Equations and Symmetry Reduction on the Lattice / Frank W. Nijhoff8:
Lagrangian Description of Doubly Discrete Sine-Gordon Type Models / Nadja Kutz9:
Quantum Systems / III:
Spectra of Quantum Integrals / Johannes Kellendonk10:
Algebraic Quantization of Integrable Models in Discrete Space-Time / Ludwig D. Faddeev ; Alexander Yu. Volkov11:
Affine Toda Field Theory as a Three-dimensional Integrable System / Rinat M. Kashaev ; Nikolai Yu. Reshetikhin12:
Quantum Hyperbolic Invariants of Knots / 13:
Charge Transport in the Discretized Landau Model / Thomas Richter14:
Index
List of contributors
Introduction / Alexander I. Bobenko ; Ruedi Seiler
Geometry / I:
43.

図書

図書
by Uwe Franz and René Schott
出版情報: Dordrecht : Kluwer, c1999  vii, 227 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 490
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Preface
Introduction / 1:
Preliminaries on Lie groups / 2:
Hopf algebras, quantum groups and braided spaces / 3:
Stochastic Processes on quantum groups / 4:
Markov Structure of quantum Levy Processes / 5:
Diffusions on braided spaces / 6:
Evolution equations and Levy processes on quantum groups / 7:
Gauss Laws in the sense of Bernstein on quantum groups / 8:
Phase retrieval for probability distributions on quantum groups / 9:
Limit theorems on quantum groups / 10:
Bibliography
Index
Preface
Introduction / 1:
Preliminaries on Lie groups / 2:
44.

図書

図書
Akademii︠a︡ nauk Ukraïnsʹkoï RSR ; Instytut matematyky (Akademii︠a︡ nauk Ukraïnsʹkoï RSR)
出版情報: Киев : Наукова думка, 1965-  v. ; 21-27 cm
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45.

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図書
David A. Cox, Sheldon Katz
出版情報: Providence, R.I. : American Mathematical Society, c1999  xxi, 469 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 68
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Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
Hodge theory and Yukawa couplings
Moduli spaces Gromov-Witten invariants
Quantum cohomology Localization
Quantum differential equations
The mirror theorem Conclusion
Singular varieties
Physical theories
Bibliography
Index
Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
46.

図書

図書
edited by Silvio Levy
出版情報: Cambridge [England] : Cambridge University Press, 1999  x, 331 p., [4] p. of col. plates ; 25 cm
シリーズ名: Mathematical Sciences Research Institute publications ; 35
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47.

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図書
Erwin Kreyszig
出版情報: New York : John Wiley & Sons, c1999  xvi, 1156, 97, 20 p. ; 26-27 cm
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How to Use this Student Solutions Manual and Study Guide
Ordinary Differential Equations (ODEs) / Part A:
First-Order ODEs / Chapter 1:
Second-Order Linear ODEs / Chapter 2:
Ordinary Differential Equations (Ode's)
First-Order ODE's / Chapter 3:
Higher Order Linear ODEs
Second Order Linear ODE's / Chapter 4:
Systems of ODEs. Phase Plane. Qualitative Methods
Higher Order Linear ODE's
Systems of ODE's Phase Plane, Qualitative Methods / Chapter 5:
Series Solutions of ODEs. Special Functions
Series Solutions of ODE's Special Functions / Chapter 6:
Laplace Transforms
Linear Algebra, Vector Calculus / Part B:
Linear Algebra: Matrices, Vectors, Determinants: Linear Systems / Chapter 7:
Matrices, Vectors, Determinants. Linear Systems / Chapter 8:
Linear Algebra: Matrix Eigenvalue Problems
Vector Differential Calculus: Grad, Div, Curl / Chapter 9:
Vector Integral Calculus: Integral Theorems / Chapter 10:
Vector Differential Calculus. Grad, Div, Curl / Part C:
Fourier Analysis, Partial Differential Equations
Fourier Series, Integrals, and Transforms / Chapter 11:
Vector Integral Calculus. Integral Theorems
Partial Differential Equations (PDE 's) / Chapter 12:
Fourier Analysis. Partial Differential Equations / Chapter 13:
Complex Numbers and Functions
Complex Integration / Chapter 14:
Power Series, Taylor Series / Chapter 15:
Partial Differential Equations (PDEs) / Chapter 16:
Laurent Series: Residue Integration
Conformal Mapping / Part D:
Complex Analysis
Complex Analysis and Potential Theory / Chapter 18:
Numerical Analysis Software / Part E:
Numerics in General / Chapter 19:
Numerical Linear Algebra / Chapter 20:
Numerics for ODE 's and PDE 's / Chapter 21:
Optimization, Graphs / Part F:
Laurent Series. Residue Integration
Unconstrained Optimization: Linear Programming / Chapter 22:
Graphs, Combinatorial Optimization / Chapter 23:
Probability / Part G:
Statistics
Data Analysis / Chapter 24:
Numeric Analysis
Probability Theory
Mathematical Statistics / Chapter 25:
References / Appendix 1:
Numeric Linear Algebra / Appendix 2:
Answers to Odd-Numbered Problems
Auxiliary Material / Appendix 3:
Numerics for ODEs and PDEs
Additional Proofs / Appendix 4:
Tables / Appendix 5:
Index
Unconstrained Optimization. Linear Programming
Graphs and Combinatorial Optimization
Probability, Statistics
Data Analysis. Probability Theory
Photo Credits
How to Use this Student Solutions Manual and Study Guide
Ordinary Differential Equations (ODEs) / Part A:
First-Order ODEs / Chapter 1:
48.

図書

図書
by Volodymyr Koshmanenko
出版情報: Dordrecht ; Boston : Kluwer, 1999  viii, 308 p.
シリーズ名: Mathematics and its applications ; v. 474
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Preface to the English Edition
Introduction
Quadratic Forms and Linear Operators / 1:
Singular Quadratic Forms / 2:
Singular Perturbations of Self-Adjoint Operators / 3:
Applications to Quantum Field Theory / 4:
References
Subject Index
Notation
Preface to the English Edition
Introduction
Quadratic Forms and Linear Operators / 1:
49.

図書

図書
Herbert Meschkowski.Translated by Robert Schlapp
出版情報: Edinburgh ; London : Oliver & Boyd, 1968  ix, 174 p ; 19 cm
シリーズ名: University mathematical texts ; 37
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50.

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図書
by Claude E. Shannon and Warren Weaver
出版情報: Urbana : University of Illinois Press, 1964, c1949  125 p. ; 24 cm
シリーズ名: Illini books ; IB-13
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目次情報:
Recent contributions to the mathematical theory of communication / by W. Weaver
The mathematical theory of communication / by C.E. Shannon
Recent contributions to the mathematical theory of communication / by W. Weaver
The mathematical theory of communication / by C.E. Shannon
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