MATHEMATICAL SOFTWARE FOR MANAGEMENT
THE AIM OF THE COURSE IS TO SHOW PROBLEMS OCCURING FROM THE CONCRETE PROBLEM SOLUTION BY A COMPUTER, SUPPLYING EFFECTIVE AND EFFICIENT METHODS AND ALGORITHMS FOR MAIN COMPUTATIONAL KERNELS OF APPLICATIONS.
Knowledge and understanding: students should know basic Sofware mathematic elements and MATLAB language
Applying knowledge and understanding: students should be able to apply the discussed numerical techniques to the analysis and solution of economic and financial problems.
Making judgements: students should be able to recognize the computational techniques required to solve the mathematical model which describes a problem arising in economics, management and finance.
Communication skills: students should clearly describe the methodologies adopted for solving the exercises in the written exam, and answer in a clear and reasoned way to the questions of the oral exam.
Learning skills: students should be able to show a good learning ability, by widening, for example, their knowledge with use of relevant bibliographic references .
Functions. limits. continuity and differentiability of real-valued functions of a single variable. derivatives, graphing. Linear algebra: systems of linear equations, vector and matrix calculus. Functions of several variables: partial derivatives. Integrals: analytical and computational techniques.
THE COURSE CONTENT CAN BE APPROXIMATIVELY SPLIT INTO THE FOLLOWING FOUR BLOCKS:
I BLOCK (12 HOURS)
THE ERRORS: MAIN SOURCES OF ERRORS IN THE RESOLUTION OF A REAL PROBLEM BY COMPUTER; ILLCONDITIONED PROBLEMS; INSTABILITY OF AN ALGORITHM.
II BLOCK(12 HOURS)
THE MATLAB SYSTEM AND ITS LANGUAGE.
III BLOCK (36 HOURS)
NUMERICAL LINEAR ALGEBRA: VECTORS AND MATRIX NORMS; DIRECT METHODS: BACK AND FORWARD-SUBSTITUTION METHODS; GAUSSIAN ELIMINATION AND PIVOTING STRATEGY; LU FACTORIZATION. ITERATIVE METHODS. CONDITION NUMBER. CONSTRUCTION OF THE RELATED SOFTWARE ELEMENTS. DATA FITTING: LAGRANGE INTERPOLATION; POLYNOMIAL INTERPOLATION; SPLINE INTERPOLATION. DATA SMOOTING: FUNCTION MODELS AND RESIDUAL NORM. LEAST SQUARE. NORMAL EQUATIONS; QR FACTORIZATION .
IV BLOCK (12 HOURS)
CASE-STUDY SOLVED BY MATLAB PROGRAMS AND GRAPHIC INTERFACES
THE DIDACTIC METHODOLOGY IS BASED ON AN INDUCTIVE APPROACH, SUGGESTING THE SPECIFIC PROBLEM SOLVING AND CASE-STUDY, BY THE USE OF TOOLS FOR THE SOFTWARE DEVELOPMENT AND RESULTS VISUALIZATION
MOLER C., Numerical Computing with Matlab, SIAM, L.E.
The final exam consists of written part and an an oral part. The written part contains two exercises. The former requires competence in linear algebra, the latter concerns interpolation or approximation problems. During the written part, books are forbidden. The PC with Language MATLAB is required. The time allocated for completion 1 hour. If the written part mark is sufficient, the student will hold the oral part. Both the written and the oral part marks contribute to the final mark.