Lectures
Lectures
Linear Algebra and Calculus
Linear Algebra and Calculus
International Doctoral Program in Economics - Scuola Superiore Sant'Anna
International Doctoral Program in Economics - Scuola Superiore Sant'Anna
AY 2016/2017
AY 2016/2017
Real and Complex Numbers (Rudin - Chap. 1)
Functions (Rudin - Chap. 2)
Vector Spaces (Lang - Chap. I)
Exercises: Rudin (Chap. 1: 1, 4, 5, 8), Lang (§ I-1: 1, 8c, 9b, 12)
Basic Topology (Rudin - Chap. 2)
Vector Spaces (Lang - Chap. I)
Exercises: Rudin (Chap. 2: 4, 5, 8), Lang (§ I-2: 1g, 3c, 5f, 7)
Basic Topology (Rudin - Chap. 2)
Numerical Sequences and Series (Rudin - Chap. 3)
Exercises: Rudin (Chap. 3: 2, 6), Lang (§ I-4: 2)
Matrices (Lang - Chap. II)
Continuity (Rudin - Chap. 4)
Exercises: Rudin (Chap. 4: 3, 4, 14), Lang (§ II-1-Matrices: 5, 10; § II-1-Dimension: 4, 6; § II-3: 8, 11, 16)
Linear Mappings (Lang - Chap. III)
Differentiation (Rudin - Chap. 5)
Exercises: Lang (§ III-2: 1, 3, 5, 15, 18; § III-4: 2, 7, 14)
Linear Maps and Matrices (Lang - Chap. IV)
The Riemann Integral (Rudin - Chap. 6)
Exercises: Lang (§ IV-1: 1; § IV-2: 1, 4; § IV-3: 1a, 2, 8, 11), Rudin (Chap. 6: 2, 15-first part only)
Scalar Products and Orthogonality (Lang - Chap. V)
Functions of Several Variables (Rudin - Chap. 9)
Exercises: Lang (§ V-1: 1, 2; § V-2: 0, 5; § V-3: 1c, 1f, 3, 4a, 5a; § V-4: 5a; § V-7: 2; § V-8: 1a, 1b), Rudin (Chap. 9: 21, 23)
Determinants (Lang - Chap. VI)
Eigenvectors and Eigenvalues (Lang - Chap. VIII)
Exercises: Lang (§ VI-2: 1; § VI-3: 1b, 1e, 2b, 2f, 2h, ; § VI-4: 1b; § VI-6: 1a, 1e, 1i, 2a, 2e, 2i; § VI-7: 2; § VI-8: 1b, 1e, 3a; § VI-9: 1, 2, 5; § VIII-1: 3; § VIII-2: 3a, 4b, 5a, 6b, 8c)
Eigenvectors and Eigenvalues (Lang - Chap. VIII)
Polynomials and Matrices, Triangulations of Matrices and Linear Maps, Polynomials and Primary Decomposition (Lang - Chap. IX-XI)
Exercises: Lang (§ VIII-4: 16a, 16b, 16e; § IX-2: 1; § X-1: 2; § XI-1: 1b, 1d)
Static Models and Comparative Statics (de La Fuente - § 2.11, Chap. 5)