Lectures

Linear Algebra and Calculus

International Doctoral Program in Economics - Scuola Superiore Sant'Anna

AY 2013/2014

02/10/2013 - 09:00-13:00 (Aula 1-Toscanelli)

• Sets (§ 1.1), Logic (§ 1.2)

• Relations (§ 1.3), Functions (§ 1.4)

• Algebraic Structures (§ 1.5)

• Real Numbers (§ 1.6), Complex Numbers (§ 1.7)

Exercises

03/10/2013 - 09:00-13:00 (Aula 6)

• Metric and Normed Spaces (§ 2.1)

• Sequences in Metric Spaces (§ 2.2), Real-Valued Sequences (§ 2.3)

• Topology (§ 2.4)

• Limits of Functions (§ 2.5)

Exercises

04/10/2013 - 09:00-13:00 (Aula 1-Toscanelli)

• Continuity (§ 2.6), Completeness (§ 2.7)

• Compactness (§ 2.8)

• Connectedness (§ 2.9)

• Equivalent Metrics and Norms (§ 2.10), Continuity of Correspondences (§ 2.11)

Exercises

07/10/2013 - 09:00-13:00 (Aula 6)

• Linear Independence and Bases (§ 3.1)

• Linear Transformations (§ 3.2)

• Isomorphisms and Matrix Representations (§ 3.3)

• Determinants (extra)

Exercises

08/10/2013 - 09:00-13:00 (Aula 2-Toscanelli)

• Linear Mappings between Normed Spaces (§ 3.4)

• Change of Basis and Similarity (§ 3.5)

• Eigenvalues and Eigenvectors (§ 3.6)

• Jordan Normal Form (extra)

Exercises

10/10/2013 - 09:00-13:00 (Aula 2-Toscanelli)

• Scalar Products (extra), Quadratic Forms (§ 6.A)

• Differentiable Univariate Real Functions (§ 4.1), Partial and Directional Derivatives (§ 4.2)

• Differentiability (§ 4.3)

• Continuous Differentiability (§ 4.4), Homogeneous Functions (§ 4.5)

Exercises

11/10/2013 - 09:00-13:00 (Aula 2-Toscanelli)

• Systems of Linear Equations (first part of § 5.1)

• Linear Models (second part of § 5.1)

• Comparative Statics and the Implicit-Function Theorem (§ 5.2)

• Existence of Equilibrium (§ 5.3), Problems (§ 5.4)

Exercises