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  1. Courses

CALCULUS - 86017

courses
ID:
86017
Dettaglio:
SSD: Mathematics for Economics, Actuarial Studies and Finance Duration: 72 CFU: 9
Located in:
BERGAMO
Url:
Course Details:
ECONOMICS - 86-R/PERCORSO COMUNE Year: 1
Year:
2025
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Overview

Date/time interval

Primo Semestre (15/09/2025 - 19/12/2025)

Syllabus

Course Objectives

To be able to work with single value function, to know the concept of derivability of single value function and its applications (max and min of a function, Taylor expansion), the Riemann integral and basics of linear algebra. After completing the course the student will be able to apply the basic calculation techniques for resolving standard problems related to the concepts learned.

Course Prerequisites

To be admitted to the written part, students need to fulfill additional training obligation of mathematics.
For the mandatory preparatory requirements, consult the website of the degree course.

Teaching Methods

Lectures: the notes of the lectures are available in the elearning after the lectures.
Tutoring: in weekly meetings the tutor will propose excercises and activity to further develop the concept explained during the lectures.
Elearning : in the platform Moodle the students can find materials and communications related to the course and the exam.

Assessment Methods

Written test (mandatory): test of 65 minutes with 12 multiple choice or open questions. The allocation of points to the script is done as follows: 1 point for each correct answer, 0 or -1 points for every wrong answer depending of the type of question. The results are posted on the bulletin board of the course with the indication AMMESSO ALL'ORALE, NON AMMESSO ALL'ORALE. Complete evaluations are published in the elearning course. Oral test (mandatory): admitted to the oral the students with minimum score of 15/30. The schedule of the oral test is published on the notice board of the course as well as ratings. Students enrolled in individual courses may occur at the specified time for the oral. Normally you can not take the oral test in a different session than the one where it was claimed the script . Final grade: vote exam dependent on the overall assessment. At the end of the 2/3 of the course it is provided the first partial test on differential calculus of functions of one variable and integration. At the end of the course there will be a second partial test of linear algebra and multivariable functions. At the second partial test students who have taken part in the first partial test are admitted and have obtained a score of not less than 15/30 (the full grade will be calculated as the weighted average of the two votes: 2/3 for the first, 1/3 for the second). Both tests are allowed for students in debt.


Contents

Real functions of a real variable: Limits, continuous function. Derivability. Monotonicity, concavity and convexity. Evaluation of minimum, maximum and inflection points. Taylor formula. Riemann integral, primitive and their computation. Real functions of real variables: Directional derivatives. Partial derivatives. Evaluation of minimum, maximum and saddle points. Linear algebra: Vectors and matrices. Determinant of a matrix and how to compute the inverse of a matrix. Linear spaces, linear dependence, linear independence and rank. Solving linear systems, Rouché-Capelli theorem, Cramer theorem.

Online Resources

  • E-learning
  • Leganto - Reading lists

Degrees

Degrees

ECONOMICS - 86-R 
Bachelor's Degree
3 years
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People

People

NARDELLI Carla
Gruppo 13/STAT-04 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE
AREA MIN. 13 - Scienze economiche e statistiche
Settore STAT-04/A - Metodi matematici dell'economia e delle scienze attuariali e finanziarie
Professori Associati
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Other

Main module

CALCULUS
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