# Course Materials

## EC9A0 course outline and notes

Greek alphabet (for mathematically inclined economists)

1. Matrix algebra: (Peter J. Hammond)
A. Linear systems: Gaussian elimination, echelon form, linear dependence, rank
B. Determinants, Cramer's rule, inverses
C. Quadratic forms: Eigenvalues, diagonalization, linear constraints
D. Ordinary least squares estimation.
Readings: EMEA chs. 15, 16; FMEA ch.1
Matrix algebra slides, Part A
Matrix algebra slides, Part B
Matrix algebra slides, Part C
Matrix algebra slides, Part D

2. Difference and differential equations: (Peter J. Hammond)
Readings: FMEA chs. 11, 5, 6, 7.
Difference equation slides, Part A
Difference equation slides, Part B
Difference equation slides, Part C
Differential equation slides

3. Real Analysis: (Pablo Beker)
Metric and normed spaces, sequences, limits, open and closed sets, continuity, subsequences, compactness.
Readings: lecture notes, FMEA ch. 13.
Slides: Real Analysis
Lecture Notes: Real Analysis

4. Unconstrained optimization: (Pablo Beker)
Concave and convex functions, Weierstrass' theorem, first- and second-order conditions, envelope theorems.
Readings: lecture notes; FMEA chs. 2, 3. Simon and Blume (ch. 18)
Slides: Unconstrained Optimisation
Lecture Notes: Unconstrained Optimisation

5. Constrained Optimisation: (Pablo Beker)
(a) Constraint qualifications,
(b) Kuhn/Tucker Theorem, first- and second-order conditions;
Readings: lecture notes; EMEA, Simon and Blume (chs. 19, 30) and Mas-Colell et al (Section M of Mathematical Appendix)
Slides: Constrained Optimisation with Equality Constraints.
Slides: Constrained Optimisation with Inequality Constraints.
Lecture Notes: Constrained Optimisation I
Lecture Notes: Constrained Optimisation II

6. Theorem of the Maximum and Envelope Theorem (Pablo Beker)
(a) Correspondences: upper and lower hemi-continuity
(b) Comparative statics and Berge's maximum theorem
Readings: chapter 3 in Stokey and Lucas.
Slides: Theorem of the Maximum and Envelope Theorem>
Lecture Notes: Theorem of the Maximum and Envelope Theorem

7. Fixed Point Theorems: (Pablo Beker)
(a) Contraction Mapping Theorem
(b) Brouwer's Fixed Point Theorem
(c) Kakutani's Fixed Point Theorem
Readings: chapter 3 in Stokey and Lucas, FMEA (ch. 14)
Slides: Fixed Point Theorems
Lecture Notes: Fixed Point Theorems

8. Calculus of Variations and Optimal Control: (Peter J. Hammond)