| Introduction |
| 1. | Review of some basic logic, matrix algebra, and calculus |
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1.1 | Logic: basics and proof by induction |
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1.2 | Matrices: determinant, inverse, and rank |
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1.3 | Solving systems of linear equations: matrix inversion and Cramer's rule |
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1.4 | Intervals and functions |
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1.5 | Calculus: one variable |
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1.6 | Calculus: many variables |
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1.7 | Graphical representation of functions |
| 2. | Topics in multivariate calculus |
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2.1 | Introduction to multivariate calculus |
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2.2 | The chain rule |
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2.3 | Derivatives of functions defined implicitly |
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2.4 | Differentials and comparative statics |
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2.5 | Homogeneous functions |
| 3. | Concavity and convexity |
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3.1 | Concave and convex functions of a single variable |
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3.2 | Quadratic forms |
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3.2.1 | Quadratic forms: definitions |
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3.2.2 | Quadratic forms: conditions for definiteness |
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3.2.3 | Quadratic forms: conditions for semidefiniteness |
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3.3 | Concave and convex functions of many variables |
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3.4 | Quasiconcavity and quasiconvexity |
| 4. | Optimization |
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4.1 | Optimization: introduction |
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4.2 | Optimization: definitions |
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4.3 | Existence of an optimum |
| 5. | Optimization: interior optima |
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5.1 | Necessary conditions for an interior optimum |
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5.2 | Local optima |
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5.3 | Conditions under which a stationary point is a global optimum |
| 6. | Optimization: equality constraints |
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6.1 | Two variables, one constraint |
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6.1.1 | Optimization with an equality constraint: necessary conditions for an optimum for a function of two variables |
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6.1.2 | Optimization with an equality constraint: interpretation of Lagrange multipliers |
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6.1.3 | Optimization with an equality constraint: sufficient conditions for a local optimum for a function of two variables |
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6.1.4 | Optimization with an equality constraint: conditions under which a stationary point is a global optimum |
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6.2 | Optimization with equality constraints: n variables, m constraints |
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6.3 | The envelope theorem |
| 7. | Optimization: the Kuhn-Tucker conditions for problems with inequality constraints |
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7.1 | Optimization with inequality constraints: the Kuhn-Tucker conditions |
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7.2 | Optimization with inequality constraints: the necessity of the Kuhn-Tucker conditions |
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7.3 | Optimization with inequality constraints: the sufficiency of the Kuhn-Tucker conditions |
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7.4 | Optimization with inequality constraints: nonnegativity conditions |
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7.5 | Optimization: summary of conditions under which first-order conditions are necessary and sufficient |
| 8. | Differential equations |
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8.1 | Differential equations: introduction |
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8.2 | First-order differential equations: existence and stability of solutions |
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8.3 | Separable first-order differential equations |
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8.4 | Linear first-order differential equations |
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8.5 | Differential equations: phase diagrams for autonomous equations |
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8.6 | Second-order differential equations |
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8.7 | Systems of first-order linear differential equations |
| 9. | Difference equations |
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9.1 | First-order difference equations |
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9.2 | Second-order difference equations |