Exam (elaborations) ECONOMIC250math

Course Information Mathematics for Economics and Finance (SECS-S/06) 12 ECTS – 84 hours Lesson period: 1st year, 2nd semester, a.y. Professor Information Prof. Francesco Rania Department of Law, Economy and Sociology Website: Email: Phone: Office hours: during the lesson period; before and after the lessons and every month before the examination Course Description The course aims to provide mathematical tools in Linear Algebra, Mathematical Analysis, and Financial Mathematics to model and solve basic economic and financial problems. Course goals and Expected Learning Outcomes Upon course completion, a student will be able to: • Know and apply the tools of Mathematical Analysis • Understand and use the basic concepts of linear algebra and matrices, including linear transformations, eigenvectors and the characteristic polynomial • Know and apply arithmetic and geometric progressions, series, sequence; • Describe and solve simple static and dynamic problems in the economic and financial field; • Acknowledge and represent an equilibrium problem and decision problem in the economic and financial field. Program Module 1 Numerical sets; Arithmetic operations; Solving equations; Simple inequalities; Calculating percentage. Set theory; propositions, theorems, connectives, implications, necessary and sufficient conditions. Functions; Composition of functions; Inverse function; Graphs. Topology of R; Euclidean metrics; Relationships between point and set. Function of one real variable; Elementary functions; Limits (notes); Continuous functions; Derivative of function; Rules for finding the derivative; Taylor polynomial; Free and constrained Optimization; Absolute minimum and maximum. Module 2 Capitalization and actualization; Interest and discount; Compounding interest; Equivalent rates; Present value of a complex transaction; Incomes and loans; Amortization plains. Functions of several variables; Case n=2; Level curves; Continuity and derivability; Partial derivate; Quadratic Forms. Weierstrass Theorem; Fermat Theorem; Sufficient condition to calculate the local minimum and maximum; Constrained optimization; Lagrange method; KuhnTucker conditions. Vector Space Rn; linearly independent vectors; Bases; Linear transformations; Kernel and Image. Matrix Algebra; Square matrices; Determinants; Inverse matrix; Rank of matrix; Systems of linear equations; Gauss method. Eigenvectors and the characteristic polynomial; Diagonal matrix. Indefinite integrals; differentiation and integration; Rules for finding integrals; Definite integrals; Improper integrals. Difference equations of the first and second order; Differential equations of the first and second order. Linear programming; Graphical method. Expected student workload Approximately 210 hours. Teaching methods - Lectures - Case studies - Exercises during the classroom lessons Learning resources (textbooks, eventual further reading, …) Textbook - K. Sydsaeter, P. Hammond, A. Strom, Metodi Matematici per l’Analisi Economica e Finanziaria, Pearson Italia, 2015. Further reading - L. Peccati, S. Salsa, A. Squellati, Matematica per l'economia e l'azienda, Terza Edizione, Egea Editore, Milano. - A. Torriero, M. Scovenna, L. Scaglianti, Manuale di Matematica, Metodi e applicazioni, Cedam, 2013. - M. Micocci, G.B. Masala, Metodi e strumenti quantitativi per il risk management, Carocci editore 2012 (Parte Prima). - C.P. Simon, L.E. Blume, Matematica 1 per l’Economia e le Scienze Sociali, Università Bocconi Editore, 2002. - C.P. Simon, L.E. Blume, Matematica 2 per l’Economia e le Scienze Sociali, Università Bocconi Edito