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1.

図書

図書
by Hassler Whitney
出版情報: Princeton, N.J. : Princeton University Press, 1957  xv, 387 p ; 24 cm
シリーズ名: Princeton mathematical series ; 21
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目次情報: 続きを見る
Preface
Introduction
The general problem of integration / A:
The integral as a function of the domain / 1:
Polyhedral chains / 2:
Two continuity hypotheses / 3:
A further continuity hypothesis / 4:
Some examples / 5:
The case r = n / 6:
The r-vector of an oriented r-cell / 7:
On r-vectors and boundaries of (r + 1)-cells / 8:
Grassmann algebra / 9:
The dual algebra / 10:
Integration of differential forms / 11:
Some classical topics / B:
Grassmann algebra in metric oriented n-space / 12:
The same, n = 3 / 13:
The differential of a mapping / 14:
Jacobians / 15:
Transformation of the integral / 16:
Smooth manifolds / 17:
Particular forms of integrals in 3-space / 18:
The Theorem of Stokes / 19:
The exterior differential / 20:
Some special formulas in metric oriented E[superscript 3] / 21:
An existence theorem / 22:
De Rham's Theorem / 23:
Indications of general theory / C:
Normed spaces of chains and cochains / 24:
Continuous chains / 25:
On 0-dimensional integration / 26:
Classical theory / Part I:
Multivectors / Chapter I:
Multicovectors
Properties of V[subscript r] and V[superscript r]
Alternating r-linear functions
Use of coordinate systems
Exterior products
Interior products
n-vectors in n-space
Simple multivectors
Linear mappings of vector spaces
Duality
Euclidean vector spaces
Mass and comass
Mass and comass of products
On projections
Differential forms / Chapter II:
The differential of a smooth mapping
Some properties of differentials
Smooth mappings
The inverse and implicit function theorems
A representation of vectors and covectors
The tangent space of a smooth manifold
Differential forms in smooth manifolds
A characterization of the exterior differential
Riemann integration theory / Chapter III:
The r-vector of an oriented r-simplex
The r-vector of an r-chain
Integration over cellular chains
Some properties of integrals
Relation to the Riemann integral
Integration over open sets
The transformation formula
Proof of the transformation formula
Transformation of the Riemann integral
Integration in manifolds
Stokes' Theorem for a parallelepiped
A special case of Stokes' Theorem
Sets of zero s-extent
Stokes' Theorem for standard domains
Proof of the theorem
Regular forms in Euclidean space
Regular forms in smooth manifolds
Stokes' Theorem for standard manifolds
The iterated integral in Euclidean space
Manifolds in Euclidean space / Chapter IV:
The imbedding theorem
The compact case
Separation of subsets of E[superscript m]
Regular approximations
Proof of Theorem 1A, M compact
Admissible coordinate systems in M
Proof of Theorem 1A, M not compact
Local properties of M in E[superscript m]
On n-directions in E[superscript m]
The neighborhood of M in E[superscript m]
Projection along a plane
Triangulation of manifolds
The triangulation theorem
Outline of the proof
Fullness
Linear combinations of edge vectors of simplexes
The quantities used in the proof
The complex L
The complex L*
The intersections of M with L*
The complex K
Imbedding of simplexes in M
The complexes K[subscript p]
Cohomology in manifolds
[mu]-regular forms
Closed forms in star shaped sets
Extensions of forms
Elementary forms / 27:
Certain closed forms are derived / 28:
Isomorphism of cohomology rings / 29:
Periods of forms / 30:
The Hopf invariant / 31:
On smooth mappings of manifolds / 32:
Other expressions for the Hopf invariant / 33:
General theory / Part II:
Abstract integration theory / Chapter V:
Mass of polyhedral chains
The flat norm
Flat cochains
Examples
The sharp norm
Sharp cochains
Characterization of the norms
An algebraic criterion for a multicovector
Sharp r-forms
The semi-norms [vertical bar A vertical bar superscript flat], [vertical bar A vertical bar superscript sharp] are norms
Weak convergence
Some relations between the spaces of chains and cochains
The [rho]-norms
The mass of chains
Separability of spaces of chains
Non-separability of spaces of cochains
Some relations between chains and functions / Chapter VI:
Continuous chains on the real line
0-chains in E[superscript 1] defined by functions of bounded variation
Sharp functions times 0-chains
The part
Functions of bounded variation in E[superscript 1] defined by 0-chains
Some related analytical theorems
Continuous r-chains in E[superscript n]
On compact cochains
The boundary of a smooth chain
Continuous chains in smooth manifolds
General properties of chains and cochains / Chapter VII:
Sharp functions times chains
Sharp functions times cochains
Supports of chains and cochains
On non-compact chains
On polyhedral approximations
Sharp chains at a point
Molecular chains are dense
Flat r-chains in E[superscript r-k] are zero
Flat cochains in complexes
Elementary flat cochains in a complex
The isomorphism theorem
Chains and cochains in open sets / Chapter VIII:
Chains and cochains in open sets, elementary properties
Chains and cochains in open sets, further properties
Properties of mass
On the open sets to which a chain belongs
An expression for flat chains
An expression for sharp chains
Lebesgue theory / Part III:
Flat cochains and differential forms / Chapter IX:
n-cochains in E[superscript n]
Some properties of fullness
Properties of projections
Elementary properties of D[subscript X](p, [alpha])
The r-form defined by a flat r-cochain
Flat r-forms
Flat r-forms and flat r-cochains
Flat r-direction functions
Flat forms defined by components
Approximation to D[subscript X](p) by [characters not reproducible]
Total differentiability of Lipschitz functions
On the exterior differential of r-forms
On averages of r-forms
Products of cochains
Lebesgue chains
Products of cochains and chains
Products and weak limits
Characterization of the procducts
Lipschitz mappings / Chapter X:
Affine approximations to Lipschitz mappings
The approximation on the edges of a simplex
Approximation to the Jacobian
The volume of affine approximations
A continuity lemma
Lipschitz chains
Lipschitz mappings of open sets
Lipschitz mappings and flat cochains
Lipschitz mappings and flat forms
Lipschitz mappings and sharp functions
Lipschitz mappings and products
On the flat norm of Lipschitz chains
Deformations of chains
Chains and additive set functions / Chapter XI:
On finite dimensional Banach spaces
Vector valued additive set functions
Vector valued integration
Point functions times set functions
Relations between a set function and its variation
On positive linear functionals
On bounded linear functionals
Linear functions of sharp r-forms
The sharp norm of r-vector valued set functions
Molecular set functions
Sharp chains and set functions
Bounded Borel functions times chains
The part of a chain in a Borel set
Chains and point functions
Characterization of the sharp norm
Expression for the sharp norm
Other expressions for the norm
Vector and linear spaces / Appendix I:
Vector spaces
Linear transformations
Conjugate spaces
Direct sums, complements
Quotient spaces
Pairing of linear spaces
Abstract homology
Normed linear spaces
Euclidean linear spaces
Affine spaces
Barycentric coordinates
Affine mappings
Euclidean spaces
Banach spaces
Semi-conjugate spaces
Geometric and topological preliminaries / Appendix II:
Cells, simplexes
Polyhedra, complexes
Su bdivisions
Standard subdivisions
Orientation
Chains and cochains
Boundary and coboundary
Homology and cohomology
Products in a complex
Joins
Subdivisions of chains
Cartesian products of cells
Mappings of complexes
Some properties of planes
Mappings of n-pseudomanifolds into n-space
Distortion of triangulations of E[superscript m]
Analytical preliminaries / Appendix III:
Existence of certain functions
Partitions of unity
Smoothing functions by taking averages
The Weierstrass approximation theorem
The space L[superscript 1]
Index of symbols
Index of terms
Preface
Introduction
The general problem of integration / A:
2.

図書

図書
C.T.C. Wall
出版情報: London ; New York : Academic Press, 1970  x, 280 p. ; 23 cm
シリーズ名: L.M.S. monographs ; 1
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3.

図書

図書
V.I. Arnold ; translated and edited by Richard A. Silverman
出版情報: Cambridge : MIT Press, c1973  viii, 280 p. ; 23 cm
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目次情報: 続きを見る
Preface
Frequently Used Notation
Basic Concepts / 1:
Phase Spaces and Phase Flows
Vector Fields on the Line / 2:
Phase Flows on the Line / 3:
Vector Fields and Phase Flows in the Plane / 4:
Nonautonomous Equations / 5:
The Tangent Space / 6:
Basic Theorems
The Vector Field near a Nonsingular Point / 7:
Applications to the Nonautonomous Case / 8:
Applications to Equations of Higher Order / 9:
Phase Curves of Autonomous Systems / 10:
The Directional Derivative. First Integrals / 11:
Conservative Systems with One Degree of Freedom / 12:
Linear Systems
Linear Problems / 13:
The Exponential of an Operator / 14:
Properties of the Exponential / 15:
The Determinant of the Exponential / 16:
The Case of Distinct Real Eigenvalues / 17:
Complexification and Decomplexification / 18:
Linear Equations with a Complex Phase Space / 19:
Complexification of a Real Linear Equation / 20:
Classification of Singular Points of Linear Systems / 21:
Topological Classification of Singular Points / 22:
Stability of Equilibrium Positions / 23:
The Case of Purely Imaginary Eigenvalues / 24:
The Case of Multiple Eigenvalues / 25:
More on Quasi-Polynomials / 26:
Nonautonomous Linear Equations / 27:
Linear Equations with Periodic Coefficients / 28:
Variation of Constants / 29:
Proofs of the Basic Theorems
Contraction Mappings / 30:
The Existence, Uniqueness, and Continuity Theorems / 31:
The Differentiable Manifolds / 33:
The Tangent Bundle. Vector Fields on a Manifold / 34:
The Phase Flow Determined by a Vector Field / 35:
The Index of a Singular Point of a Vector Field / 36:
Sample Examination Problems
Bibliography
Index
Preface
Frequently Used Notation
Basic Concepts / 1:
4.

図書

図書
Robert C. Gunning, general editor
出版情報: Princeton, N.J. : Princeton University Press, 1970  x, 351 p. ; 24 cm
シリーズ名: Princeton mathematical series ; 31
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5.

図書

図書
editor, E.G.D. Cohen
出版情報: Amsterdam ; Tokyo : North-Holland , New York, N.Y., U.S.A. : Sole distributor for the U.S.A. and Canada, Elsevier Science Pub. Co., 1985  x, 398 p. ; 27 cm
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6.

図書

図書
by John von Neumann ; foreword by Israel Halperin
出版情報: Princeton, N.J. : Princeton University Press, 1960  xi, 299 p. ; 24 cm
シリーズ名: Princeton mathematical series ; 25
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7.

図書

図書
Sterling K. Berberian
出版情報: New York ; Berlin ; Tokyo : Springer, c1974  ix, 345 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 15
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8.

図書

図書
Renfrey B. Potts, Robert M. Oliver
出版情報: New York : Academic Press, 1972  xi, 192 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 90
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9.

図書

図書
Morris W. Hirsch and Stephen Smale
出版情報: New York : Academic Press, c1974  xi, 358 p. ; 23 cm
シリーズ名: Pure and applied mathematics ; v. 60
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目次情報: 続きを見る
Preface
First Examples
Newton's Equation and Kepler's Law
Linear Systems with Constant Coeffecients and Real Eigenvalues
Linear Systems with Constant Coefficients and Complex Eigenvalues
Linear Systems and Exponentials of Operators
Linear Systems and Canonical Forms of Operators
Contractions and Generic Properties of Operators
Fundamental Theory
Stability of Equilibria
Differential Equations for Electrical Circuits
The Poincare-Bendixson Theorem
Ecology
Periodic Attractors
Classical Mechanics
Nonautonomous Equations and Differentiability of Flows
Perturbation Theory and Structural Stability
Elementary Facts
Polynomials
On Canonical Forms
The Inverse Function Theorem
References
Answers to Selected Problems
Index
Preface
First Examples
Newton's Equation and Kepler's Law
10.

図書

図書
V.M. Popov ; [translated by Radu Georgescu]
出版情報: Berlin ; New York : Springer , Bucureşti : Editura Academiei, 1973  400 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 204
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11.

図書

図書
Solomon Lefschetz
出版情報: New York : Academic Press, 1965  xi, 150 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 13
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12.

図書

図書
J. Kevorkian, J.D. Cole
出版情報: New York : Springer-Verlag, c1981  x, 558 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 34
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13.

図書

図書
Lars V. Ahlfors
出版情報: New York : McGraw-Hill, 1953  xi, 247 p. ; 24 cm
シリーズ名: International series in pure and applied mathematics
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14.

図書

図書
J.H. Ahlberg, E.N. Nilson, J.L. Walsh
出版情報: New York ; London : Academic Press, 1967  xi, 284 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 38
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15.

図書

図書
Edited by E.R. Caianiello
出版情報: New York : Academic Press, 1966  xiv, 342 p. ; 24 cm
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16.

図書

図書
edited by E.R. Caianiello
出版情報: New York : Academic Press, 1966  xiii, 225 p. ; 24 cm
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目次情報: 続きを見る
Preface / by E.R. Caianiello
Linear control systems; controllability / by H.S. Antosiewicz
Approximation of variational inequations / by J.P. Aubin
On the state-space theory of nonlinear systems / by A.V. Balakrishnan
Nonlinear problems posed by decision equations / by E.R. Caianiello
On a generalization of the bang-bang principle / by C. Castaing
Some computational aspects of the theory of optimal control / by W. De Back
The approximate solution of an unstable physical problem subject to constraints / by J. Douglas, Jr
Optimal control of diffusion processes / by W.H. Fleming
Convexity and control theory / by H. Halkin
Non-well-set problems and the method of quasi reversibility / by R. Lattès
On some optimization problems for linear parabolic equations / by J.L. Lions
Controllability and observability / by L. Markus
Convexity and duality / by J.J. Moreau
The first non-distributive algebra, with relations to optimization and control theory / by C. Muses
Suboptimal supervisory control / by A. Straszak
Preface / by E.R. Caianiello
Linear control systems; controllability / by H.S. Antosiewicz
Approximation of variational inequations / by J.P. Aubin
17.

図書

図書
Michael D. Canon, Clifton D. Cullum, Jr., Elijah Polak
出版情報: New York : McGraw-Hill, c1970  xii, 285 p. ; 23 cm
シリーズ名: McGraw-Hill series in systems science
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18.

図書

図書
[by] Kenneth J. Arrow [and] F.H. Hahn
出版情報: San Francisco : Holden-Day , Edinburgh : Oliver and Boyd, c1971  xii, 452 p. ; 24 cm
シリーズ名: Mathematical economics texts ; 6
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19.

図書

図書
edited by Eli Mishkin and Ludwig Braun, Jr. ; contributors, John G. Truxal ... [et al.]
出版情報: New York : McGraw-Hill, 1961  xiv, 533 p. ; 24 cm
シリーズ名: McGraw-Hill electrical and electronic engineering series
Brooklyn Polytechnic Institute series
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20.

図書

図書
E. D. Cashwell and C. J. Everett
出版情報: London : Pergamon, 1959  ix, 153 p. ; 23 cm.
シリーズ名: International tracts in computer science and technology and their application ; vol. 1
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21.

図書

図書
by Claude Chevalley
出版情報: [Tokyo] : The Mathematical Society of Japan, 1955  vi, 64 p. ; 21 cm
シリーズ名: Publications of the Mathematical Society of Japan ; 1
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22.

図書

図書
Mark A. Aiserman ... [et al.] ; translated by Scripta Technica, Inc. ; translation editor, George M. Kranc
出版情報: New York : Academic Press, 1971  xii, 433 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 79
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23.

図書

図書
by E.T. Bell
出版情報: New York ; London : McGraw-Hill, 1945  xiii, 637 p. ; 23 cm
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24.

図書

図書
Gaisi Takeuti
出版情報: Amsterdam ; New York ; Tokyo : North-Holland , New York : Sole distributors for the U.S.A. and Canada, Elsevier Science, 1987  x, 490 p. ; 23 cm
シリーズ名: Studies in logic and the foundations of mathematics ; v. 81
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25.

図書

図書
J.L. Lions, E. Magenes ; translated from the French by P. Kenneth
出版情報: Berlin ; New York : Springer-Verlag, 1972-1973  3 v. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 181-183
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26.

図書

図書
edited by K. Dietz and V. Rittenberg
出版情報: Singapore ; Philadelphia : World Scientific, c1987  viii, 201 p. ; 23 cm
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27.

図書

図書
William Fulton, Serge Lang
出版情報: New York : Springer-Verlag, c1985  x, 203 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 277
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28.

図書

図書
Winfried Scharlau
出版情報: Berlin ; New York : Springer-Verlag, 1985  x, 421 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 270
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29.

図書

図書
V.I. Arnold ; translated by Joseph Szücs ; English translation edited by Mark Levi
出版情報: New York ; Berlin : Springer-Verlag, c1983  x, 334 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 250
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目次情報: 続きを見る
Special Equations
First-Order Partial Differential Equations
Structural Stability
Perturbation Theory
Normal Forms
Local Bifurcation Theory
Samples of Examination Problems
Index
Special Equations
First-Order Partial Differential Equations
Structural Stability
30.

図書

図書
Michael Reed, Barry Simon
出版情報: New York ; Tokyo : Academic Press, c1975  xv, 361 p. ; 24 cm
シリーズ名: Methods of modern mathematical physics / Michael Reed, Barry Simon ; 2
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目次情報:
The Fourier Transform
Self-Adjointness and The Existence of Dynamics
The Fourier Transform
Self-Adjointness and The Existence of Dynamics
31.

図書

図書
Michael Reed, Barry Simon
出版情報: New York ; Tokyo : Academic Press, c1979  xv, 463 p. ; 24 cm
シリーズ名: Methods of modern mathematical physics / Michael Reed, Barry Simon ; 3
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32.

図書

図書
Akira Okubo
出版情報: Berlin : Springer-Verlag, 1980  xiii, 254 p. ; 25 cm
シリーズ名: Biomathematics ; v. 10
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33.

図書

図書
editor, G. Mayer-Kress
出版情報: Berlin ; Tokyo : Springer-Verlag, 1986  ix, 257 p. ; 25 cm
シリーズ名: Springer series in synergetics ; v. 32
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34.

図書

図書
Lars Hörmander
出版情報: Berlin ; Tokyo : Springer-Verlag, c1985  vii, 351 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 275 . The analysis of linear partial differential operators / Lars Hörmander ; 4
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Contents: Lagrangian Distributions and Fourier Integral Operators
Pseudo-Differential Operators of Principal Type
Subelliptic Operators
Uniqueness for the Cauchy Problem
Spectral Asymptotics
Long Range Scattering Theory
Bibliography
Index
Index of Notation.
Contents: Lagrangian Distributions and Fourier Integral Operators
Pseudo-Differential Operators of Principal Type
Subelliptic Operators
35.

図書

図書
H.-O. Peitgen, P.H. Richter
出版情報: Berlin ; Tokyo : Springer-Verlag, c1986  xii, 199 p., [1] leaf of plates ; 29 cm
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36.

図書

図書
Ioan Tomescu ; translated from Romanian by Robert A. Melter
出版情報: New York : Wiley, c1985  xvii, 335 p. ; 25 cm
シリーズ名: Wiley-Interscience series in discrete mathematics
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37.

図書

図書
R.K. Dodd ... [et al.]
出版情報: London ; New York : Academic Press, 1982  x, 630 p. ; 26 cm
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38.

図書

図書
editor, Y. Kuramoto
出版情報: Berlin ; Tokyo : Springer-Verlag, 1984  xi, 273 p. ; 25 cm
シリーズ名: Springer series in synergetics ; v. 24
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39.

図書

図書
Donald J. Albers, G.L. Alexanderson, Constance Reid
出版情報: New York : Springer-Verlag, c1987  63 p. ; 29 cm
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40.

図書

図書
edited by Dietrich Stauffer
出版情報: Singapore : World Scientific, 1994-  v. ; 23 cm
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41.

図書

図書
Robert M. Fano, Lan Jen Chu, Richard B. Adler
出版情報: New York ; London : Wiley, c1960  xv, 520 p. ; 24 cm
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42.

図書

図書
Albert S. Schwarz ; [translator, Silvio Levy]
出版情報: Berlin ; New York : Springer-Verlag, c1994  xi, 296 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 308
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43.

図書

図書
by Sydney Goldstein ; with special lectures by J. M. Burgers
出版情報: London ; New York : Interscience Publishers, c1960  xvi, 309 p. ; 24 cm
シリーズ名: Lectures in applied mathematics : proceedings of the Summer Seminar, Boulder, Colorado, 1957 ; v. 2
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44.

図書

図書
Serge Lang
出版情報: Reading, Mass. : Addison-Wesley Pub. Co, 1972  ix, 230 p. ; 24 cm
シリーズ名: Addison-Wesley series in mathematics ; 4166
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45.

図書

図書
H.H. Happ
出版情報: New York : Academic Press, 1971  xv, 312 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 69
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46.

図書

図書
by Raymond M. Smullyan
出版情報: Princeton, N.J. : Princeton University Press, 1961  viii, 142 p ; 26 cm
シリーズ名: Annals of mathematics studies ; no. 47
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47.

図書

図書
edited by Leon Henkin, Patrick Suppes, Alfred Tarski
出版情報: Amsterdam : North-Holland, 1959  xi, 488 p. ; 23 cm
シリーズ名: Studies in logic and the foundations of mathematics
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48.

図書

図書
Constantin Corduneanu
出版情報: New York : Academic Press, 1973  ix, 238 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 104
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49.

図書

図書
[by] Michael A. Harrison
出版情報: New York : Academic Press, 1969  x, 210 p. ; 24 cm
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50.

図書

図書
Richard K. Miller
出版情報: Menlo Park, Calif. : W.A. Benjamin, c1971  ix, 468 p. ; 23 cm
シリーズ名: Mathematics lecture note series
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