I will post slides for each class by the morning of the day of the class. The compact versions are best for printing, the complete ones best for viewing on a screen.
- Week 1 (September 5)
-
Review of logic, matrices, systems of linear equations, intervals and functions, one-variable calculus, and basic multivariate calculus.
- Week 2 (September 12)
-
Chain rule, Implicit differentiation, differentials and comparative statics, homogeneous functions
- Week 3 (September 19)
-
Concave and convex functions of a single variable, quadratic forms.
- Week 4 (September 26)
-
Quadratic forms: conditions for definiteness, Quadratic forms: conditions for semidefiniteness, Concave and convex functions of many variables.
- Week 5 (October 3)
- 2:10p-3:40p: Term test 1. 4p-5p: Quasiconcavity and quasiconvexity.
- Week 6 (October 10)
-
Optimization: introduction, Optimization: definitions, Existence of an optimum, Necessary conditions for an interior optimum, Local optima.
- Week 7 (October 17)
-
Conditions under which a stationary point is a global optimum,
Optimization with an equality constraint: necessary conditions for an optimum for a function of two variables
- Week 8 (October 24)
-
Optimization with equality constraints: interpretation of Lagrange multipliers,
sufficient conditions for a local optimum for a function of two variables,
conditions under which a stationary point is a global optimum,
n variables, m constraints,
The envelope theorem
- Week 9 (October 31)
-
Optimization with inequality constraints:
Kuhn-Tucker onditions, Necessity of Kuhn-Tucker conditions,
Sufficiency of Kuhn-Tucker conditions,
Nonnegativity conditions,
Optimization: summary of conditions under which first-order conditions are necessary and sufficient
- Week 10 (November 14)
- 2:10p-3:40p: Term test 2.
- Week 11 (November 21)
-
Differential equations: introduction,
First-order differential equations: existence of a solution,
Separable first-order differential equations,
Linear first-order differential equations,
Differential equations: phase diagrams for autonomous equations
- Week 12 (November 28)
-
Differential equations: phase diagrams for autonomous equations,
Second-order differential equations,
Systems of linear first-order differential equations