| Description |
1 online resource |
| Contents |
Machine generated contents note: Introduction -- 1. Systems of linear equations and matrices -- 1.1. Introduction -- 1.2. Linear equations and examples -- 1.3. Matrix operations -- 1.4. Rules of matrix algebra -- 1.5. Some special types of matrix and associated rules -- 2. Determinants -- 2.1. Introduction -- 2.2. Preliminaries -- 2.3. Definition and properties -- 2.4. Co-factor expansions of determinants -- 2.5. Solution of systems of equations -- 3. Eigenvalues and eigenvectors -- 3.1. Introduction -- 3.2. Definitions and illustration -- 3.3. Computation -- 3.4. Unit eigenvalues -- 3.5. Similar matrices -- 3.6. Diagonalization -- 4. Conic sections, quadratic forms and definite matrices -- 4.1. Introduction -- 4.2. Conic sections -- 4.3. Quadratic forms -- 4.4. Definite matrices -- 5. Vectors and vector spaces -- 5.1. Introduction -- 5.2. Vectors in 2-space and 3-space -- 5.3. n-Dimensional Euclidean vector spaces -- 5.4. General vector spaces -- 6. Linear transformations -- 6.1. Introduction -- 6.2. Definitions and illustrations -- 6.3. Properties of linear transformations -- 6.4. Linear transformations from Rn to Rm -- 6.5. Matrices of linear transformations -- 7. Foundations for vector calculus -- 7.1. Introduction -- 7.2. Affine combinations, sets, hulls and functions -- 7.3. Convex combinations, sets, hulls and functions -- 7.4. Subsets of n-dimensional spaces -- 7.5. Basic topology -- 7.6. Supporting and separating hyperplane theorems -- 7.7. Visualizing functions of several variables -- 7.8. Limits and continuity -- 7.9. Fundamental theorem of calculus -- 8. Difference equations -- 8.1. Introduction -- 8.2. Definitions and classifications -- 8.3. Linear, first-order difference equations -- 8.4. Linear, autonomous, higher-order difference equations -- 8.5. Systems of linear difference equations |
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Note continued: 9. Vector calculus -- 9.1. Introduction -- 9.2. Partial and total derivatives -- 9.3. Chain rule and product rule -- 9.4. Elasticities -- 9.5. Directional derivatives and tangent hyperplanes -- 9.6. Taylor's theorem: deterministic version -- 9.7. Multiple integration -- 9.8. Implicit function theorem -- 10. Convexity and optimization 244 -- 10.1. Introduction -- 10.2. Convexity and concavity -- 10.3. Unconstrained optimization -- 10.4. Equality-constrained optimization -- 10.5. Inequality-constrained optimization -- 10.6. Duality -- Introduction -- 11. Macroeconomic applications -- 11.1. Introduction -- 11.2. Dynamic linear macroeconomic models -- 11.3. Input-output analysis -- 12. Single-period choice under certainty -- 12.1. Introduction -- 12.2. Definitions -- 12.3. Axioms -- 12.4. consumer's problem and its dual -- 12.5. General equilibrium theory -- 12.6. Welfare theorems -- 13. Probability theory -- 13.1. Introduction -- 13.2. Sample spaces and random variables -- 13.3. Applications -- 13.4. Vector spaces of random variables -- 13.5. Random vectors -- 13.6. Expectations and moments -- 13.7. Multivariate normal distribution -- 13.8. Estimation and forecasting -- 13.9. Taylor's theorem: stochastic version -- 13.10. Jensen's inequality -- 14. Quadratic programming and econometric applications -- 14.1. Introduction -- 14.2. Algebra and geometry of ordinary least squares -- 14.3. Canonical quadratic programming problem -- 14.4. Stochastic difference equations -- 15. Multi-period choice under certainty -- 15.1. Introduction -- 15.2. Measuring rates of return -- 15.3. Multi-period general equilibrium -- 15.4. Term structure of interest rates -- 16. Single-period choice under uncertainty -- ̂ 16.1. Introduction -- 16.2. Motivation -- 16.3. Pricing state-contingent claims |
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Note continued: 16.4. expected-utility paradigm -- 16.5. Risk aversion -- 16.6. Arbitrage, risk neutrality and the efficient markets hypothesis -- 16.7. Uncovered interest rate parity: Siegel's paradox revisited -- 16.8. Mean[-]variance paradigm -- 16.9. Other non-expected-utility approaches -- 17. Portfolio theory -- 17.1. Introduction -- 17.2. Preliminaries -- 17.3. Single-period portfolio choice problem -- 17.4. Mathematics of the portfolio frontier -- 17.5. Market equilibrium and the capital asset pricing model -- 17.6. Multi-currency considerations |
| Summary |
The aim of this book is to bring students of economics and finance who have only an introductory background in mathematics up to a quite advanced level in the subject, thus preparing them for the core mathematical demands of econometrics, economic theory, quantitative finance and mathematical economics, which they are likely to encounter in their final-year courses and beyond. The level of the book will also be useful for those embarking on the first year of their graduate studies in Business, Economics or Finance |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Economics -- Mathematical models.
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Finance -- Mathematical models.
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Economics, Mathematical.
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BUSINESS & ECONOMICS -- Economics -- Theory.
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Economics, Mathematical
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Economics -- Mathematical models
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Finance -- Mathematical models
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| Form |
Electronic book
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| Author |
Waldron, Patrick
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| ISBN |
9780203829998 |
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0203829999 |
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