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1.

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
2.

図書

図書
Michael W. Frazier
出版情報: New York ; Tokyo : Springer, c1999  xvi, 501 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
Background: Complex Numbers and Linear Algebra / 1:
Real Numbers and Complex Numbers / 1.1:
Complex Series, Euler's Formula, and the Roots of Unity / 1.2:
Vector Spaces and Bases / 1.3:
Linear Transformations, Matrices, and Change of Basis / 1.4:
Diagonalization of Linear Transformations and Matrices / 1.5:
Inner Products, Orthonormal Bases, and Unitary Matrices / 1.6:
The Discrete Fourier Transform / 2:
Basic Properties of the Discrete Fourier Transform / 2.1:
Translation-Invariant Linear Transformations / 2.2:
The Fast Fourier Transform / 2.3:
Wavelets on $bZ_N$ / 3:
Construction of Wavelets on $bZ_N$: The First Stage / 3.1:
Construction of Wavelets on $bZ_N$: The Iteration Step / 3.2:
Examples and Applications / 3.3:
Wavelets on $bZ$ / 4:
$ ell ^2(bZ)$ / 4.1:
Complete Orthonormal Sets in Hilbert Spaces / 4.2:
$L^2([- pi , pi ))$ and Fourier Series / 4.3:
The Fourier Transform and Convolution on $ ell ^2(bZ)$ / 4.4:
First-Stage Wavelets on $bZ$ / 4.5:
The Iteration Step for Wavelets on $bZ$ / 4.6:
Implementation and Examples / 4.7:
Wavelets on $bR$ / 5:
$L^2(bR)$ and Approximate Identities / 5.1:
The Fourier Transform on $bR$ / 5.2:
Multiresolution Analysis and Wavelets / 5.3:
Construction of Multiresolution Analyses / 5.4:
Wavelets with Compact Support and Their Computation / 5.5:
Wavelets and Differential Equations / 6:
The Condition Number of a Matrix / 6.1:
Finite Difference Methods for Differential Equations / 6.2:
Wavelet-Galerkin Methods for Differential Equations / 6.3:
Bibliography
Index
Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
3.

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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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
4.

図書

図書
Jean Dieudonné
出版情報: Paris : Hermann, c1969  207 p. ; 23 cm
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5.

図書

図書
[by] Richard E. Williamson [and] Hale F. Trotter
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, [1974]  ix, 630 p. ; 25 cm
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目次情報:
04104-08 Trade Math One (20 Hours)
Builds on trainees' basic math skills to solve trade-reproblems
Covers calculations using denomiand volume calculations, English-metric system conversbasic geometry, and calculation of stretchouts
04104-08 Trade Math One (20 Hours)
Builds on trainees' basic math skills to solve trade-reproblems
Covers calculations using denomiand volume calculations, English-metric system conversbasic geometry, and calculation of stretchouts
6.

図書

図書
[by] Richard C. MacCamy, Victor J. Mizel
出版情報: London,[New York] : Macmillan, c1969  xiii, 561 p ; 24 cm
シリーズ名: Textbooks in applied mathematics
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7.

図書

図書
Philip E. Gill, Walter Murray, Margaret H. Wright
出版情報: Redwood City, Calif. : Addison-Wesley Pub. Co., Advanced Book Program, c1991  xvii, 426 p. ; 24 cm
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8.

図書

図書
Steven Roman
出版情報: New York : Springer, c2005  xvi, 482 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 135
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Preface to the Second Edition
Preface to the First Edition
Preliminaries
Algebraic Structures / Part 1:
Basic Linear Algebra / Part I:
Vector Spaces / 1:
Subspaces
Direct Sums
Spanning Sets and Linear Independence
The Dimension of a Vector Space
Ordered Bases and Coordinate Matrices
The Row and Column Spaces of a Matrix
The Complexification of a Real Vector Space
Exercises
Linear Transformations / 2:
Isomorphisms
The Kernel and Image of a Linear Transformation
Linear Transformations from F[superscript n] to F[superscript m]
The Rank Plus Nullity Theorem
Change of Basis Matrices
The Matrix of a Linear Transformation
Change of Bases for Linear Transformations
Equivalence of Matrices
Similarity of Matrices
Similarity of Operators
Invariant Subspaces and Reducing Paris
Topological Vector Spaces
Linear Operators on V[superscript C]
The Isomorphism Theorems / 3:
Quotient Spaces
The Universal Property of Quotients and the First Isomorphism Theorem
Quotient Spaces, Complements and Codimension
Additional Isomorphism Theorems
Linear Functionals
Dual Bases
Reflexivity
Annihilators
Operator Adjoints
Modules I: Basic Properties / 4:
Modules
Motivation
Submodules
Spanning Sets
Linear Independence
Torsion Elements
Free Modules
Homomorphisms
Quotient Modules
The Correspondence and Isomorphism Theorems
Direct Sums and Direct Summands
Modules Are Not As Nice As Vector Spaces
Modules II: Free and Noetherian Modules / 5:
The Rank of a Free Module
Free Modules and Epimorphisms
Noetherian Modules
The Hilbert Basis Theorem
Modules over a Principal Ideal Domain / 6:
Annihilators and Orders
Cyclic Modules
Free Modules over a Principal Ideal Domain
Torsion-Free and Free Modules
Prelude to Decomposition: Cyclic Modules
The First Decomposition
A Look Ahead
The Primary Decomposition
The Cyclic Decomposition of a Primary Module
The Primary Cyclic Decomposition Theorem
The Invariant Factor Decomposition
The Structure of a Linear Operator / 7:
A Brief Review
The Module Associated with a Linear Operator
Orders and the Minimal Polynomial
Cyclic Submodules and Cyclic Subspaces
Summary
The Decomposition of V[subscript tau]
The Rational Canonical Form
Eigenvalues and Eigenvectors / 8:
The Characteristic Polynomial of an Operator
Geometric and Algebraic Multiplicities
The Jordan Canonical Form
Triangularizability and Schur's Lemma
Diagonalizable Operators
Projections
The Algebra of Projections
Resolutions of the Identity
Spectral Resolutions
Projections and Invariance
Real and Complex Inner Product Spaces / 9:
Norm and Distance
Isometries
Orthogonality
Orthogonal and Orthonormal Sets
The Projection Theorem and Best Approximations
Orthogonal Direct Sums
The Riesz Representation Theorem
Structure Theory for Normal Operators / 10:
The Adjoint of a Linear Operator
Unitary Diagonalizability
Normal Operators
Special Types of Normal Operators
Self-Adjoint Operators
Unitary Operators and Isometries
The Structure of Normal Operators
Matrix Versions
Orthogonal Projections
Orthogonal Resolutions of the Identity
The Spectral Theorem
Spectral Resolutions and Functional Calculus
Positive Operators
The Polar Decomposition of an Operator
Topics / Part II:
Metric Vector Spaces: The Theory of Bilinear Forms / 11:
Symmetric, Skew-Symmetric and Alternate Forms
The Matrix of a Bilinear Form
Quadratic Forms
Orthogonal Complements and Orthogonal Direct Sums
Hyperbolic Spaces
Nonsingular Completions of a Subspace
The Witt Theorems: A Preview
The Classification Problem for Metric Vector Spaces
Symplectic Geometry
The Structure of Orthogonal Geometries: Orthogonal Bases
The Classification of Orthogonal Geometries: Canonical Forms
The Orthogonal Group
The Witt's Theorems for Orthogonal Geometries
Maximal Hyperbolic Subspaces of an Orthogonal Geometry
Metric Spaces / 12:
The Definition
Open and Closed Sets
Convergence in a Metric Space
The Closure of a Set
Dense Subsets
Continuity
Completeness
The Completion of a Metric Space
Hilbert Spaces / 13:
Infinite Series
An Approximation Problem
Hilbert Bases
Fourier Expansions
A Characterization of Hilbert Bases
Hilbert Dimension
A Characterization of Hilbert Spaces
Tensor Products / 14:
Universality
Bilinear Maps
When Is a Tensor Product Zero?
Coordinate Matrices and Rank
Characterizing Vectors in a Tensor Product
Defining Linear Transformations on a Tensor Product
The Tensor Product of Linear Transformations
Change of Base Field
Multilinear Maps and Iterated Tensor Products
Tensor Spaces
Special Multilinear Maps
Graded Algebras
The Symmetric Tensor Algebra
The Antisymmetric Tensor Algebra: The Exterior Product Space
The Determinant
Positive Solutions to Linear Systems: Convexity and Separation / 15:
Convex, Closed and Compact Sets
Convex Hulls
Linear and Affine Hyperplanes
Separation
Affine Geometry / 16:
Affine Combinations
Affine Hulls
The Lattice of Flats
Affine Independence
Affine Transformations
Projective Geometry
Operator Factorizations: QR and Singular Value / 17:
The QR Decomposition
Singular Values
The Moore-Penrose Generalized Inverse
Least Squares Approximation
The Umbral Calculus / 18:
Formal Power Series
The Umbral Algebra
Formal Power Series as Linear Operators
Sheffer Sequences
Examples of Sheffer Sequences
Umbral Operators and Umbral Shifts
Continuous Operators on the Umbral Algebra
Umbral Operators and Automorphisms of the Umbral Algebra
Umbral Shifts and Derivations of the Umbral Algebra
The Transfer Formulas
A Final Remark
References
Index
Preface to the Second Edition
Preface to the First Edition
Preliminaries
9.

図書

図書
[by] W.H. Greub
出版情報: Berlin ; New York : Springer, 1967  xiv, 434 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 97
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10.

図書

図書
Serge Lang
出版情報: Reading ; Mass : Addison-Wesley, 1969,c1971,1972  xi, 400 p. ; 24 cm
シリーズ名: Addison-Wesley series in mathematics
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