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1.

図書
図書
1. Calculus of several variables and differentiable manifolds
[by] Carl B. Allendoerfer
出版情報: New York : Macmillan, [1974]  xi, 227 p. ; 26 cm
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2.

図書
図書
2. Multivariable mathematics : linear algebra, differential equations, calculus
[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
3.

図書
図書
3. Introduction to calculus and analysis (v. 2)
Richard Courant and Fritz John, with the assistance of Albert A. Blank, Alan Solomon
出版情報: New York : Wiley-Interscience, c1974  xxiii,954 p. ill. ; 23 cm
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目次情報: 続きを見る
Relations Between Surface and Volume Integrals: Connection Between Line Integrals and Double Integrals in the Plane
Vector Form of the Divergence Theorem / Stokes's Theorem
Formula for Integration by Parts in Two Dimensions: / Green's Theorem
The Divergence Theorem Applied to the Transformation of Double Integrals
Area Differentiation
Interpretation of the Formulae of Gauss and Stokes by Two-Dimensional Flows
Orientation of Surfaces
Integrals of Differential Forms and of Scalars over Surfaces
Gauss's and Green's Theorems in Space
Appendix: General Theory of Surfaces and of Surface Integrals.- Differential Equations: The Differential Equations for the Motion of a Particle in Three Dimensions
The General Linear Differential Equation of the First Order
Linear Differential Equations of Higher Order
General Differential Equations of the First Order
Systems of Differential Equations and Differential Equations of Higher Order
Integration by the Method of Undermined Coefficients
The Potential of Attracting Charges and Laplace's Equation
Further Examples of Partial Differential Equations from Mathematical Physics
Calculus of Variations: Functions and Their Extreme Values of a Functional
Generalizations
Problems Involving Subsidiary Conditions. Lagrange Multipliers
Functions of a Complex Variable: Complex Functions Represented by Power Series
Foundations of the General Theory of Functions of a Complex Variable
The Integration of Analytic Functions
Cauchy's Formula and Its Applications
Applications to Complex Integration (Contour Integration)
Many-Valued Functions and Analytic Extension.
List of Biographical Dates
Index
Relations Between Surface and Volume Integrals: Connection Between Line Integrals and Double Integrals in the Plane
Vector Form of the Divergence Theorem / Stokes's Theorem
Formula for Integration by Parts in Two Dimensions: / Green's Theorem
4.

図書
図書
4. The fractional calculus : theory and applications of differentiation and integration to arbitrary order
Keith B. Oldham, Jerome Spanier
出版情報: New York : Academic Press, 1974  xiii, 234 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 111
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目次情報: 続きを見る
Preface
Overview / 1：
Methods of Operator Approximation in System Modelling / I：
Nonlinear Operator Approximation with Preassigned Accuracy / 2：
Introduction / 2.1：
Generic formulation of the problem / 2.2：
Operator approximation in space C([0; 1]) / 2.3：
Operator approximation in Banach spaces by polynomial operators / 2.4：
Approximation on compact sets in topological vector spaces / 2.5：
Approximation on noncompact sets in Hilbert spaces / 2.6：
Special results for maps into Banach spaces / 2.7：
Concluding remarks / 2.8：
Interpolation of Nonlinear Operators 65 / 3：
Lagrange interpolation in Banach spaces / 3.1：
Weak interpolation of nonlinear operators / 3.3：
Some related results / 3.4：
Realistic Operators and their Approximation / 3.5：
Formalization of concepts related to description of real-world objects / 4.1：
Approximation of RÂícontinuous operators / 4.3：
Methods of Best Approximation for Nonlinear Operators / 4.4：
Best Approximation of nonlinear operators in Banach spaces: Deterministic case / 5.1：
Estimation of mean and covariance matrix for random vectors / 5.3：
Best Hadamard-quadratic approximation / 5.4：
Best polynomial approximation / 5.5：
Best causal approximation / 5.6：
Best hybrid approximations / 5.7：
II Optimal Estimation of Random Vectors / 5.8：
Computational Methods for Optimal Filtering of Stochastic Signals / 6：
Optimal linear Filtering in Finite dimensional vector spaces / 6.1：
Optimal linear Filtering in Hilbert spaces / 6.3：
Optimal causal linear Filtering with piecewise constant memory / 6.4：
Optimal causal polynomial Filtering with arbitrarily variable memory / 6.5：
Optimal nonlinear Filtering with no memory constraint / 6.6：
Computational Methods for Optimal Compression and Reconstruction of Random Data / 6.7：
Standard Principal Component Analysis and Karhunen-Loeeve transform (PCA{KLT) / 7.1：
Rank-constrained matrix approximations / 7.3：
Generic PCA{KLT / 7.4：
Optimal hybrid transform based on Hadamard-quadratic approximation / 7.5：
Optimal transform formed by a combination of nonlinear operators / 7.6：
Optimal generalized hybrid transform / 7.7：
Bibliography / 7.8：
Index
Preface
Overview / 1：
Methods of Operator Approximation in System Modelling / I：
5.

図書
図書
5. Calculus and analytic geometry. 3d ed
Schwartz, Abraham
出版情報: New York : Holt, Rinehart and Winston, [c1974]  xv, 1140, 134 p ; 25 cm
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6.

図書
図書
6. Analytic geometry and the calculus. 3rd ed.
A.W. Goodman
出版情報: New York : Macmillan, ｃ1974  xxii, 919, A1-112 p. ; 24 cm
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7.

図書
図書
7. Real and complex analysis. 2nd ed
Walter Rudin
出版情報: New York ; London : McGraw-Hill, 1974  xii, 452 p. ; 24 cm
シリーズ名: McGraw-Hill series in higher mathematics
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目次情報: 続きを見る
Preface Prologue: The Exponential Function
Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, 8] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises / Chapter 1：
Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises / Chapter 2：
L p -Spaces Convex functions and inequalities TheL p -spaces Approximation by continuous functions Exercises / Chapter 3：
Elementary Hilbert Space Theory Inner products and linear functionals Orthonormal sets Trigonometric series Exercises / Chapter 4：
Examples of Banach Space Techniques Banach spaces Consequences of Baire's theorem Fourier series of continuous functions Fourier coefficients ofL1-functions The Hahn-Banach theorem An abstract approach to the Poisson integral Exercises / Chapter 5：
Complex Measures Total variation Absolute continuity Consequences of the Radon-Nikodym theorem Bounded linear functionals onL p The Riesz representation theorem Exercises / Chapter 6：
Differentiation Derivatives of measures The fundamental theorem of Calculus Differentiable transformations Exercises / Chapter 7：
Integration on Product Spaces Measurability on cartesian products Product measures The Fubini theorem Completion of product measures Convolutions Distribution functions Exercises / Chapter 8：
Fourier Transforms Formal properties The inversion theorem The Plancherel theorem The Banach algebraL1 Exercises / Chapter 9：
Elementary Properties of Holomorphic Functions Complex differentiation Integration over paths The local Cauchy theorem The power series representation The open mapping theorem The global Cauchy theorem The calculus of residues Exercises / Chapter 10：
Harmonic Functions The Cauchy-Riemann equations The Poisson integral The mean value property Boundary behavior of Poisson integrals Representation theorems Exercises / Chapter 11：
The Maximum Modulus Principle Introduction The Schwarz lemma The Phragmen-Lindelouml;f method An interpolation theorem A converse of the maximum modulus theorem Exercises / Chapter 12：
Approximation by Rational Functions Preparation Runge's theorem The Mittag-Leffler theorem Simply connected regions Exercises / Chapter 13：
Conformal Mapping Preservation of angles Linear fractional transformations Normal families The Riemann mapping theorem The classL Continuity at the boundary Conformal mapping of an annulus Exercises / Chapter 14：
Zeros of Holomorphic Functions Infinite Products The Weierstrass factorization theorem An interpolation problem Jensen's formula Blaschke products The Muuml;ntz-Szas theorem Exercises / Chapter 15：
Analytic Continuation Regular points and singular points Continuation along curves The monodromy theorem Construction of a modular function The Picard theorem Exercises / Chapter 16：
H p -Spaces Subharmonic functions The spacesH p and N The theorem of F. and M. Riesz Factorization theorems The shift operator Conjugate functions Exercises / Chapter 17：
Elementary Theory of Banach Algebras Introduction The invertible elements Ideals and homomorphisms Applications Exercises / Chapter 18：
Holomorphic Fourier Transforms Introduction Two theorems of Paley and Wiener Quasi-analytic classes The Denjoy-Carleman theorem / Chapter 19：
Preface Prologue: The Exponential Function
Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, 8] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises / Chapter 1：
Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises / Chapter 2：
8.

図書
図書
8. Real and complex analysis. 2nd ed (hard ; pbk.)
Walter Rudin
出版情報: New Delhi : Tata McGraw-Hill, 1974  xii, 452 p. ; 23 cm
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