93,85 zł

Mathematical Economics Dover Publications Inc.

Książki / Literatura obcojęzyczna

1. Introduction 1.1 Mathematical Economics 1.2 Outline of the Book 1.3 Notes on the Literature Part I: Optimizing Theory 2. The General Optimizing Problem 2.1 Introduction 2.2 The General Structure 2.3 Constraints and the Feasible Set 2.4 The General Optimizing Problem 2.5 The General Solution Principle 2.6 Conditions for a Global Optimum 2.7 Important Special Cases 2.8 Direct Solutions or Optimal Condtions? Exercises 3. The Theory of Linear Programming 3.1 Introduction 3.2 The Feasible Set 3.3 Duality 3.4 The Optimum Conditions 3.5 Basic Solutions 3.6 The Basis Theorem 3.7 Interpretation of the Dual Variables Further Reading Exercises 4. Classical Calculus Methods 4.1 Introduction 4.2 The Lagrangean Function 4.3 Interpretation of the Lagrange Multipliers 4.4 A Geometrical Note 4.5 Second Order Conditions for the Classical Case 4.6 The Substitution Effect of Neoclassical Demand Theory 4.7 Global Optimum Condtions in the Classical Problem Exercises 5. Advanced Optimizing Theory 5.1 Introduction 5.2 Nonnegative Variables 5.3 Inequality Constraints 5.4 Saddle Points and Duality 5.5 The Dual Variables 5.6 The Minimax Theorem 5.7 Exercises of Optimal Solutions Further Reading Exercises Part II: Static Economic Models 6. Input-Output and Related Models 6.1 Input-Output Models 6.2 The Closed Model 6.3 The Leontief Open Model 6.4 Direct and Indirect Input Requirements 6.5 Factor Intensity in the Leontief Model 6.6 A Labor Theory of Value 6.7 The Substitution Theorem 6.8 Matrix Multipliers Further Reading Exercises 7. Linear Optimizing Models 7.1 Activity Analysis of Production 7.2 The Production Set 7.3 Efficient Production 7.4 Constrained Production 7.5 Consumption as an Activity Further Reading Exercises 8. Nonlinear Optimizing Models 8.1 Introduction 8.2 Neoclassical Demand Theory 8.3 Convexity Proof of the Substitution Theorem 8.4 The Neoclassical Transformation Surface 8.5 Returns to Scale 8.6 Relative Factor Intensity 8.7 Generalized Production Theory Further Reading 9. General Equilibrium 9.1 Equilibrium in a Market Economy 9.2 Walras' Law and the Budget Constraint 9.3 The Excess Demand Theorem 9.4 The Walras-Wald Model 9.5 The Arrow-Debreu-McKenzie Model Further Reading Part III: Dynamic Economic Models 10. Balanced Growth 10.1 Introduction 10.2 A Leontief-Type Model 10.3 The Von Neumann Growth Model 10.4 The Von Neumann-Leontief Model 10.5 General Balanced Growth Models Further Reading 11. Efficient and Optimal Growth 11.1 Efficiency and Optimality in Dynamic Models 11.2 The Principle of Optimality 11.3 Efficient Growth 11.4 Properties of Efficient Paths 11.5 A Turnpike Theorem 11.6 An Explicit Turnpike Example Further Reading 12. Stability 12.1 The Concept of Stability 12.2 Stability Analysis 12.3 Market Stability 12.4 Stability of Decentralized Economic Policy Part IV: MATHEMATICAL REVIEWS RI. Fundamental Ideas R1.1 Sets R1.2 Ordered and Quasi-Ordered Sets R1.3 Cartesian Products and Spaces R1.4 "Functions, Transformations, Mappings, Correspondences" R1.5 Closedness and Boundedness R1.6 Complex Numbers Exercises R2. Linear Algebra R2.1 Vectors R2.2 Fundamental Theorem of Vector Spaces R2.3 Basis and Rank R2.4 Sums and Direct Sums R2.5 Scalar Products R2.6 Complex Vectors R2.7 Matrices R2.8 Matrix Algebra R2.9 Matrix-Vector Products and Linear Transformations R2.10 Partitioned Matrices R2.11 Vector Sets Exercises R3. Linear Equations and Inequalities R3.1 Introduction R3.2 The Rank of Matrix R3.3 Homogeneous Equations R3.4 Nonhomogeneous Equations R3.5 Nonnegative Vectors and Vector Inequalities R3.6 Fundamental Theorem on Linear Inequalities R3.7 Results on Linear Equations and Inequalities Exercises R4. Convex Sets and Cones R4.1 Geometric Ideas R4.2 Convex Sets R4.3 Separating and Supporting Hyperplanes R4.4 Extreme Points R4.5 Convex Cones R4.6 Finite Cones and Homogeneous Inequalities R4.7 The Dual Cone Exercises R5. Square Matrices and Characteristic Roots R5.1 Introduction R5.2 Determinants and Cramer's Rule R5.3 The Inverse of a Square Matrix R5.4 Charateristic Roots and Vectors   R5.5 Diagonalization R5.6 Convergence of Matrix Series R5.7 Charateristic Row Vectors R5.8 Numerical Examples Exercises R6. Symmetric Matrices and Quadratic Forms R6.1 Symmetric Matrices R6.2 Quadratic Forms R6.3 Constrained Quadratic Forms Exercises R7. Semipositive and Dominant Diagonal Matrices R7.1 Introduction R7.2 Indecomposability R7.3 Properties of Semipositive Square Matrices R7.4 Properties of Dominant Diagonal Matrices R7.5 Proofs Exercises R8. Continuous Functions R8.1 Introduction R8.2 Derivatives and Differentials R8.3 Some Mapping Relationships R8.4 Maxima and Minima R8.5 Convex and Concave Functions R8.6 Homogeneous and Homothetic Functions R8.7 The Brouwer Fixed Point Theorem R8.8 Linear Homogeneous Vector-Valued Functions Exercises R9. Point-to-Set Mappings R9.1 Introduction R9.2 The Graph of a Mapping R9.3 Continuity&

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105,51 zł

Linear Algebra Dover Publications Inc.

Książki / Literatura obcojęzyczna

chapter 1 DETERMINANTS 1.1. Number Fields 1.2. Problems of the Theory of Systems of Linear Equations 1.3. Determinants of Order n 1.4. Properties of Determinants 1.5. Cofactors and Minors 1.6. Practical Evaluation of Determinants 1.7. Cramer's Rule 1.8. Minors of Arbitrary Order. Laplace's Theorem 1.9. Linear Dependence between Columns Problemschapter 2 LINEAR SPACES 2.1. Definitions 2.2. Linear Dependence 2.3. "Bases, Components, Dimension" 2.4. Subspaces 2.5. Linear Manifolds 2.6. Hyperplanes 2.7. Morphisms of Linear Spaces Problemschapter 3 SYSTEMS OF LINEAR EQUATIONS 3.1. More on the Rank of a Matrix 3.2. Nontrivial Compatibility of a Homogeneous Linear System 3.3. The Compatability Condition for a General Linear System 3.4. The General Solution of a Linear System 3.5. Geometric Properties of the Solution Space 3.6. Methods for Calculating the Rank of a Matrix Problemschapter 4 LINEAR FUNCTIONS OF A VECTOR ARGUMENT 4.1. Linear Forms 4.2. Linear Operators 4.3. Sums and Products of Linear Operators 4.4. Corresponding Operations on Matrices 4.5. Further Properties of Matrix Multiplication 4.6. The Range and Null Space of a Linear Operator 4.7. Linear Operators Mapping a Space Kn into Itself 4.8. Invariant Subspaces 4.9. Eigenvectors and Eigenvalues Problemschapter 5 COORDINATE TRANSFORMATIONS 5.1. Transformation to a New Basis 5.2. Consecutive Transformations 5.3. Transformation of the Components of a Vector 5.4. Transformation of the Coefficients of a Linear Form 5.5. Transformation of the Matrix of a Linear Operator *5.6. Tensors Problemschapter 6 THE CANONICAL FORM OF THE MATRIX OF A LINEAR OPERATOR 6.1. Canonical Form of the Matrix of a Nilpotent Operator 6.2. Algebras. The Algebra of Polynomials 6.3. Canonical Form of the Matrix of an Arbitrary Operator 6.4. Elementary Divisors 6.5. Further Implications 6.6. The Real Jordan Canonical Form *6.7. "Spectra, Jets and Polynomials" *6.8. Operator Functions and Their Matrices Problemschapter 7 BILINEAR AND QUADRATIC FORMS 7.1. Bilinear Forms 7.2. Quadratic Forms 7.3. Reduction of a Quadratic Form to Canonical Form 7.4. The Canonical Basis of a Bilinear Form 7.5. Construction of a Canonical Basis by Jacobi's Method 7.6. Adjoint Linear Operators 7.7. Isomorphism of Spaces Equipped with a Bilinear Form *7.8. Multilinear Forms 7.9. Bilinear and Quadratic Forms in a Real Space Problemschapter 8 EUCLIDEAN SPACES 8.1. Introduction 8.2. Definition of a Euclidean Space 8.3. Basic Metric Concepts 8.4. Orthogonal Bases 8.5. Perpendiculars 8.6. The Orthogonalization Theorem 8.7. The Gram Determinant 8.8. Incompatible Systems and the Method of Least Squares 8.9. Adjoint Operators and Isometry Problemschapter 9 UNITARY SPACES 9.1. Hermitian Forms 9.2. The Scalar Product in a Complex Space 9.3. Normal Operators 9.4. Applications to Operator Theory in Euclidean Space Problemschapter 10 QUADRATIC FORMS IN EUCLIDEAN AND UNITARY SPACES 10.1. Basic Theorem on Quadratic Forms in a Euclidean Space 10.2. Extremal Properties of a Quadratic Form 10.3 Simultaneous Reduction of Two Quadratic Forms 10.4. Reduction of the General Equation of a Quadratic Surface 10.5. Geometric Properties of a Quadratic Surface *10.6. Analysis of a Quadric Surface from Its Genearl Equation 10.7. Hermitian Quadratic Forms Problemschapter 11 FINITE-DIMENSIONAL ALGEBRAS AND THEIR REPRESENTATIONS 11.1. More on Algebras 11.2. Representations of Abstract Algebras 11.3. Irreducible Representations and Schur's Lemma 11.4. Basic Types of Finite-Dimensional Algebras 11.5. The Left Regular Representation of a Simple Algebra 11.6. Structure of Simple Algebras 11.7. Structure of Semisimple Algebras 11.8. Representations of Simple and Semisimple Algebras 11.9. Some Further Results Problems*Appendix CATEGORIES OF FINITE-DIMENSIONAL SPACES A.1. Introduction A.2. The Case of Complete Algebras A.3. The Case of One-Dimensional Algebras A.4. The Case of Simple Algebras A.5. The Case of Complete Algebras of Diagonal Matrices A.6. Categories and Direct SumsHINTS AND ANSWERSBIBLIOGRAPHYINDEX

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