MATHEMATICS FOR BUSINESS AND FINANCE - A
MATHEMATICS FOR BUSINESS AND FINANCE - A
Academic year 2017/2018
- Course ID
- Teaching staff
- Mariacristina Uberti (Lecturer)
Prof. Luisa Tibiletti (Lecturer)
Prof. Alberto Albano (Lecturer)
Riccardo Coda (Assistant technician)
Alessandro Migliavacca (Assistant technician)
Paolo Rosano (Assistant technician)
Prof. Alberto Turigliatto (Assistant technician)
- 1st year
- Course disciplinary sector (SSD)
- SECS-S/06 - metodi matematici dell'economia e delle scienze att. e finanz.
- Formal authority
- Type of examination
- Successful course completion requires knowledge of the subjects of analysis developed in the course of Mathematics.
Sommario del corso
Course objectivesThe aim of the course is to present a tool-kit to face economic and financial environments, putting stress on business applications.
Results of learning outcomesThrough an intuitive and direct explanation of concepts and mathematical tools, the course allows students to acquire basic knowledge for approaching the study of main economic and business problems. In particular, at the end of the course, the student is expected to be capable of:
- knowing the techniques and the basic mathematical tools commonly used in the solution of problems of economic and financial nature;
- using such techniques and tools to formalize and solve problems;
- being able to communicate the results obtained using a clear and appropriate mathematical notation and language.
Course deliveryThe course is organized into 84 hours of lectures.
Learning assessment methodsThe exam consists in a compulsory written test (lasting about 1 hour and 30 minutes) and it is aimed at ascertaining the students' ability to:
1) briefly introduce the main concepts and tools developed in the course;
2) use these tools to solve practical exercises.
This aim is achieved through the formulation of:
1) two open-ended questions, of a theoretical nature, with the purpose of illustrating one or more concepts developed during lessons
2) twelve multiple choice questions, with the purpose of carrying out short numerical exercises that require the application of the acquired competences.
The answers are to be crossed on the question paper. In addition, it is mandatory to give on a white sheet a detailed report about the given answers.
Support activitiesDuring the course, tutoring activities will be carried out. Students are encouraged to pose questions on unclear topics delivered during the lessons.
Functions of one variable
Definition, domain, codomain, image, graph of a function. Elementary functions and injective, surjective, inverse, composite functions. Bounded, monotone, convex functions. Maximum and minimum of a function.
Limits and continuity
Notion of limit. Computation of limits and fundamental theorems. Important limits and indeterminate forms. Continuous functions and theorems.
Differential calculus and applications
Notion of derivative and its geometrical meaning, higher-order derivatives, rules of derivation. Derivatives of elementary functions, of inverse functions and composite functions. Theorems of differential calculus. Monotonicity and convexity tests. Optimum problems. Study of functions.
Notions of linear algebra
Vectors, matrices and operations.
Functions of two variables
Definition and domain. Graph and level curves. Continuity and derivability. Partial derivatives and gradient. Differentiability and tangent plane. Problems of unconstrained optimum.
Economic and business applications.
Fixed costs, variable costs and revenues. Demand function. Income taxes. Production optimization. Profit maximization. Elasticity.
Accumulation and discount. Standard systems of financial laws. Annuities and amortization plans.
Suggested textbooks and readingsPECCATI L., SALSA S., SQUELLATI A.M., Mathematics for Economics and Business, EGEA, Milano, 2016.
MATTALIA C., TIBILETTI L., UBERTI M., Basic Finance for Business, E-book McGraw Hill, 2014, ISBN 9788838674549.
MATTALIA C., Exercises of Mathematics for Economics and Business, Celid, Torino, 2011.
Furher reading on Financial calculus:
E. CASTAGNOLI, M. CIGOLA, L. PECCATI, Financial Calculus with Applications, Milano, EGEA, 2013