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# 30400 - MATHEMATICS AND STATISTICS - MODULE 1 (MATHEMATICS)

BEMACS
Department of Decision Sciences

Course taught in English

Go to class group/s: 25

BEMACS (8 credits - I sem. - OB  |  SECS-S/06)
Course Director:
EMANUELE BORGONOVO

Classes: 25 (I sem.)
Instructors:
Class 25: EMANUELE BORGONOVO

Course Objectives
The purpose of this course is to teach the student the basic notions of calculus and linear algebra together with the basic techniques and applications that accompany them.

Course Content Summary
• Mathematical logics: propositional logic, Truth tables. Statements and proof, Quantifiers.
• Structures. The set R: real numbers, operations, properties. The set R^n: vectors, operations, properties.
• Functions. Composite function, inverse function. Real functions of one real variable: domain, maxima/minima, convexity, other properties. Real functions of n real variables: domain, maxima/minima, convexity, other properties.
• Sequences of real numbers: definition and properties. Limits of sequences and their computation. Recurring sequences.
• Numerical series. Series with non-negative terms, series with terms of indefinite sign.
• Limits and continuity for functions of one or n real variables.
• One-variable differential calculus. Derivative. Differentiability. Differentiation rules and theorems. Higher-order derivatives. Taylor formula. Optimization conditions.
• Integral calculus. Fundamental theorem of Calculus. Improper integrals. Numerical quadrature.
• Linear algebra. Subspaces. Linear dependence and independence. Basis and dimension of a subspace. Matrices and their operations. Determinant, rank and inverse matrix. Linear systems: discussion and structure of the solutions, solution.
• N-variable differential calculus. Partial derivatives and gradient. Differentiability. Unconstrained extrema: optimization conditions.
• Introduction to numerical analysis with Matlab (R).

Detailed Description of Assessment Methods
The exam will be written, with theoretical and computer-based questions.
Students can choose whether to take the exam with two partial, or through a final exam.
Graded assignments and homeworks will be handed out during the course.

Textbooks
• S. Cerreia Vioglio, M. Marinacci, E. Vigna, Principles of Mathematics for Economics.
• Other materials will be provided online.
Last change 10/06/2016 09:21