Updated A.Y. 2020-2021
- Integral Calculus. Definite and indefinite integrals, Integral properties, The fundamental theorem of calculus, Integration by parts and integration by substitution, Improper integrals.
- Linear Spaces. The algebra of vectors, Euclidean Spaces, Inner product, Linear independence.
- Matrices. Matrix algebra, Determinant, Inverse Matrix.
- Systems of Linear equations. The Gauss Elimination Algorithm, Rouche Capelli theorem.
- Eigenvalues and eigenvectors, Diagonalization.
- Calculus of several variables. Domain, Partial derivatives, gradient, hessian matrix. Stationary points. Countour curves.
- Unconstrained optimization. First and second order conditions
- Constrained optimization with Equality constraints. First and second order conditions
- Optimization on a set
Essential Mathematics for Economic Analysis
Carl P. Simon, Lawrence Blume, Mathematics for Economists
Available on the webpage of the course and on Teams:
- Slides of the course
- Additional Exercises
Available on Moodle:
- Self-check tests are uploaded on Friday every week
The final Syllabus will be available only at the end of the course.
You can find below a detailed program which will be update on a daily basis during the teaching period.
22/02/2021 Antiderivative. Theorem: if a function has one antiderivative, then it has infinitely many antiderivatives (with proof). Indefinite integrals: definition. Integrals of Elementary Functions.
23/02/2020 Integrals of Elementary Functions., Integration by substitution, integration by parts, Approximation of an area by Riemann sums
24/02/2020 Definite integral, Properties of definite integrals, The Fundamental Theorem of Calculus: statement and applications, The Mean Value Theorem: statement and geometric interpretation.
01/03/2020 Improper integral. Matrix, Operations with matrices: sum and multiplication by a scalar (definition and properties). The null matrix.
02/03/2020 The transpose of a matrix, Vectors, operations with vectors: sum, multiplication by a scalar, inner product (definition and properties). Linear combination of vectors. The standard vectors in R^n: definition and properties (with proof). Matrix-vector multiplication (definition and properties). The identity matrix: definition and property (with proof).
03/03/2020 Matrix product (definition and properties), Matrix product is not commutative (two counterexamples), Diagonal, Lower Triangular and Upper Triangular matrices. Inverse of a matrix (definition), The inverse of a matrix is unique (with proof), Inverse of a 2x2 matrix (with proof), necessary and sufficient condition for invertibility, The determinant of a matrix: cofactor expansion by rows and by columns.