- Docente: Maria Letizia Guerra
- Credits: 8
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Rimini
- Corso: First cycle degree programme (L) in Economics of Tourism (cod. 0908)
Learning outcomes
At the end of the course the student is familiar with the mathematics foundations, in particular with basic linear algebra, fundamentals of functions and one variable differential calculus, in order to approach the economics, financial and corporate applications.
Course contents
Basic Elements (the same as approached in the pre-courses)
Elementary theory of real numbers. Relations and functions. Intervals, upper and lower bounds. Maximum and minimum of intervals. Algebraic, logarithmic, exponential and radical equations and disequalities. Graphic solution of equations. Analytic geometry: equations of lines, parabolas, hyperbole, circumference.
Calculus
Real functions of one real variable: properties, composition, inverse. Increasing and decreasing functions. Polynomial, logarithmic, exponential, rational and radical functions.
Limits in a real point and to infinite. Local and global continuity. Weierstrass theorem and theorem about the existence of roots for a continuous function.
Derivatives: properties and rules. Geometric meaning of the first derivative. Non constrained optimization: existence of maximum and minimum. Concavity and convexity. Qualitative analysis of the graphs of simple functions.
Matrix and vector algebra
Introductory matrix theory and operations with matrixes. Sarrus and Laplace rules for the determinant computation of square matrixes. Properties of the determinant.
Invertible matrix, necessary and sufficient conditions for invertibility. Inverse matrix and rank.
Eigenvalues and eigenvectors of a square matrix.
Systems of linear equations: Cramer and Rouchè-Capelli theorems. Homogeneous systems. Solutions of systems depending on a parameter.
Readings/Bibliography
S. Waner and S.R. Costenoble: “Finite Mathematics and Applied Calculus”, 3rd Edition, Brooks/Cole, 2004
C. Cleaves and M.Hobbs “Business Math”, Complete w/CD & Study Guide & PH Math Tutor (7th Edition), Hardcover, Prentice Hall
Assessment methods
The written part of foundations of mathematics can be done through two partial exams, the first one in November and the second one in January. The examination consists in an obligatory written part and in an optional oral part. The final vote is the score obtained in the written part if the student doesn't want the oral examination
Teaching tools
Frontal lecturers and exercises in collaboration with students
Office hours
See the website of Maria Letizia Guerra