000			04485nam a22002057a 4500
005			20250617112657.0
008			250617b |||||||| |||| 00| 0 eng d
020			_a9781032698946
082			_a330.0151 _bTOD
100			_aToda, Alexis Akira _923499
245			_aEssential mathematics for economics
260			_bCRC Press _aBoca Raton _c2025
300			_axxi, 285 p.
365			_aGBP _b49.99
500			_aTable of Contents: 0. Roadmap. Section I. Introduction to Optimization. 1. Existence of Solutions. 1.1. Introduction. 1.2. The Real Number System. 1.3. Convergence of Sequences. 1.4. The Space rn. 1.5. Topology of rn. 1.6. Continuous Functions. 1.7. Extreme Value Theorem. 1.A. Topological Space. 2. One-Variable Optimization. 2.1. Introduction. 2.2. Differentiation. 2.3. Necessary Condition. 2.4. Mean Value and Taylor’s Theorem. 2.5. Sufficient Condition. 2.6. Optimal Savings Problem. 3. Multi-Variable Unconstrained Optimization. 3.1. Introduction. 3.2. Linear Maps and Matrices. 3.3. Differentiation. 3.4. Chain Rule. 3.5. Necessary Condition. 4. Introduction to Constrained Optimization. 4.1. Introduction. 4.2. One Linear Constraint. 4.3. Multiple Linear Constraints. 4.4. Karush-Kuhn-Tucker Theorem. 4.5. Inequality and Equality Constraints. 4.6. Constrained Maximization. 4.7. Dropping Nonnegativity Constraints. Section II. Matrix and Nonlinear Analysis. 5. Vector Space, Matrix, and Determinant. 5.1. Introduction. 5.2. Vector Space. 5.3. Solving Linear Equations. 5.4. Determinant. 6. Spectral Theory. 6.1. Introduction. 6.2. Eigenvalue and Eigenvector. 6.3. Diagonalization. 6.4. Inner Product and Norm. 6.5. Upper Triangularization. 6.6. Positive Definite Matrices. 6.7. Second-Order Optimality Condition. 6.8. Matrix Norm and Spectral Radius. 7. Metric Space and Contraction. 7.1. Metric Space. 7.2. Completeness and Banach Space. 7.3. Contraction Mapping Theorem. 7.4. Blackwell’s Sufficient Condition. 7.5. Perov Contraction. 7.6. Parametric Continuity of Fixed Point. 8. Implicit Function and Stable Manifold Theorem. 8.1. Introduction. 8.2. Inverse Function Theorem. 8.3. Implicit Function Theorem. 8.4. Optimal Savings Problem. 8.5. Optimal Portfolio Problem. 8.6. Stable Manifold Theorem. 8.7. Overlapping Generations Model. 9. Nonnegative Matrices. 9.1. Introduction. 9.2. Markov Chain. 9.3. Perron’s Theorem. 9.4. Irreducible Nonnegative Matrices. 9.5. Metzler Matrices. Section III. Convex and Nonlinear Optimization. 10. Convex Sets. 10.1. Convex Sets. 10.2. Convex Hull. 10.3. Hyperplanes and Half Spaces. 10.4. Separation of Convex Sets. 10.5. Cone and Dual Cone. 10.6. No-Arbitrage Asset Pricing. 11. Convex Functions. 11.1. Convex and Quasi-Convex Functions. 11.2. Convexity-Preserving Operations. 11.3. Differential Characterization. 11.4. Continuity of Convex Functions. 11.5. Homogeneous Quasi-Convex Functions. 11.6. Log-Convex Functions. 12. Nonlinear Programming. 12.1. Introduction. 12.2. Necessary Condition. 12.3. Karush-Kuhn-Tucker Theorem. 12.4. Constraint Qualifications. 12.5. Saddle Point Theorem. 12.6. Duality. 12.7. Sufficient Conditions. 12.8. Parametric Differentiability. 12.9. Parametric Continuity. Section IV. Dynamic Optimization. 13. Introduction to Dynamic Programming. 13.1. Introduction. 13.2. Knapsack Problem. 13.3. Shortest Path Problem. 13.4. Optimal Savings Problem. 13.5. Optimal Stopping Problem. 13.6. Secretary Problem. 13.7. Abstract Formulation. 14. Contraction Methods. 14.1. Introduction. 14.2. Markov Dynamic Program. 14.3. Sequential and Recursive Formulations. 14.4. Properties of Value Function. 14.5. Restricting Spaces. 14.6. State-Dependent Discounting. 14.7. Weighted Supremum Norm. 14.8. Numerical Dynamic Programming. 15. Variational Methods. 15.1. Introduction. 15.2. Euler Equation. 15.3. Transversality Condition. 15.4. Stochastic Case. 15.5. Optimal Savings Problem.
520			_aEssential Mathematics for Economics covers mathematical topics that are essential for economic analysis in a concise but rigorous fashion. The book covers selected topics such as linear algebra, real analysis, convex analysis, constrained optimization, dynamic programming, and numerical analysis in a single volume. The book is entirely self-contained, and almost all propositions are proved. (https://www.routledge.com/Essential-Mathematics-for-Economics/Toda/p/book/9781032698946)
650			_aEconomics, Mathematical
650			_aEconomics--Mathematical models _91942
942			_cBK _2ddc
999			_c9919 _d9919