
Teaching Matematica generale (91765)
Primo anno di ECONOMIA AZIENDALE FROSINONE  Piazza Marzi, 1  03100 (L18), Economia e management dell'innovazione
Credits (CFU): 9,00
Program:
Structures
The set R of real numbers, its geometric representation. Operations. Order. Intervals. The real extended line. Absolute value, distance. Neighbourhoods. Left/right neighbourhoods. Neighbourhoods of minus infinity/plus infinity. Interior, exterior, boundary points. Open, closed, bounded, compact sets. Isolated, accumulation points. The set of real vectors with n components, its geometric representation for n=2,3. Linear operations, linear combinations, inner product of vectors. Order. Convex sets. Norm, distance.
Functions
The concept of function. Domain, codomain, range; image, inverse image. Injective, surjective, bijective function. Composition of functions, other operations with functions. Inverse function.
Real functions of one real variable. Natural domain, graph. Review of elementary functions. Examples in Economics, Management and Finance. Bounded functions. Monotonic functions, strictly monotonic functions. Maxima/minima: global and local. Strict maxima/minima. Concave/convex functions, strictly concave/convex functions; their maximum/minimum properties.
Sequences
Sequences of real numbers. Recursively defined sequences. Limits of sequences. Convergent, divergent, irregular sequences. Theorem on the uniqueness of the limit. Limits of elementary sequences. Simple and compound accumulation. Operations with limits, indeterminate forms. The symbols ~ and o. Calculation of limits. Comparisons among infinities and among infinitesimals. Theorem on the permanence of sign. Comparison criterion. Regularity theorem for monotonic sequences. The number e. Extension to sequences of real vectors.
Number series
The concept of series. The sequence of partial sums. Behaviour of a series; convergent, divergent, irregular series. Behaviour of the geometric series. Present value of ordinary annuities and perpetuities. Behaviour of the harmonic series. Necessary condition for convergence. Series with nonnegative terms: regularity theorem, behaviour of the generalized harmonic series, asymptotic comparison criterion, comparison criterion. Series with terms of indefinite sign: simple convergence and absolute convergence.
Limits of functions and continuity
Limits of functions of one real variable (bilateral, from the left, from the right; from above, from below). Vertical and horizontal asymptotes. Theorem on the uniqueness of the limit. Limits of elementary functions. Operations with limits, indeterminate forms. The symbols ~ and o. Calculation of limits. Change of variable. Notable limits. Theorem on the permanence of sign. Comparison criterion. Continuity for functions of one real variable. Points of discontinuity. Continuity of elementary functions. Weierstrass’s theorem, zerovalue theorem (Bolzano’s theorem), intermediatevalue theorem (Darboux’s theorem).
Onevariable differential calculus
Difference quotient, derivative at a point; geometric meaning, equation of the tangent line. Left and right derivative at a point; corners. The derivative function. Derivatives of elementary functions. Rules on derivatives. Higher derivatives. Examples in Economics, Management and Finance. Relationship between the existence of a finite derivative and continuity. Differentiability, differential. Relationship between the existence of a finite derivative and differentiability.
Stationary points. Necessary condition for points of local maximum/minimum (Fermat’s theorem). Rolle’s theorem. Lagrange’s mean value theorem. Monotonicity/strict monotonicity test on an interval. First sufficient condition for points of local maximum/minimum. Taylor’s formula and Maclaurin’s formula of order n, with Peano’s remainder. Maclaurin’s formulae for elementary functions. Second sufficient condition for points of local maximum/minimum. Determination of the points of global maximum/minimum. Concavity/strict concavity test on an interval. Maximum/ minimum properties for concave/convex functions. Study of the graph of a function. Applications: the graph of the DCF of an investment, the graph of the logistic curve.
Integral Calculus
Riemann’s integral. Properties of the integral. Mean value theorem. The Fundamental Theorem of Calculus. The indefinite integral. Properties of the indefinite integral. Linearity and the decomposition method. Integration by parts. Integration by substitution. Improper integrals. Properties of improper integrals.
Linear algebra
Linear spaces, subspaces. Linear independence, linear dependence. Basis, dimension. Matrices. Linear operations with matrices. Rowcolumn product. Transpose matrix. Determinant of a square matrix: definition, first Laplace’s theorem, properties. Inverse matrix of a square matrix; definition, existence, uniqueness, explicit writing in terms of the adjoint matrix. Rank of a matrix: definition as the maximum number of linearly independent rows or columns, computation as the maximum order of nonnull minors, Kronecker’s theorem. Linear functions: definition, representation theorem, representation matrix. Linear production functions.
Linear systems: explicit writing, matrix writing. Existence of solutions: RouchéCapelli’s theorem, distinction between the determinate and the indeterminate cases. Computation of solutions: Cramer’s theorem, Cramer’s rule; extension to all linear systems. Leontief’s model, the brandtobrand transition model.
Reference books:
Textbook:
• M. Angrisani, Introduzione all’attività matematica, Edizioni CISU, 2015.
• E. Castagnoli, Algebra lineare, Edizioni Lilith, 2011.
• Materials distributed by the instructor.
Propaedeutic topics:
• M. Angrisani, P. Ferroni, Argomenti preliminari al corso di matematica generale, Kappa, 1998.

Teaching Soft Skills (91954)
Primo anno di Global economy and business (LM56), Dual Degree Unicas  Epoka University
Credits (CFU): 3,00
Program:
The course starts from the distinction between hard skills and soft skills.
Hard skills are specific and teachable. They are actual knowledge, technical or intellectual and are typically quantifiable and measurable. They include traditional knowledge areas such as the STEM subjects  Science, Technology, Engineering and Mathematics  but also encompass other measurable skills such as language proficiency and technical skills.
By contrast, soft skills are more difficult to measure and quantify. Often called interpersonal skills, they include personality traits such as critical thinking, leadership, problemsolving and life skills  which include negotiating, networking, and working with cultural diversity as well as communication and listening, etiquette, getting along with other people.
Both types of skills are necessary to successfully perform and advance in most jobs.
Presentation skills are especially important in the workplace. Knowing how to present your ideas, to a group or an individual, in a way which is both informative and persuasive, is the best tool in your arsenal for success and career advancement.
The course focus on the ability of making a successful presentation.
Reference books:
Attending students
Notes provided by the instructor and additional materials provided to prepare a specific presentation that will be selected based on the background education of students.
Nonattending students
Specific material to be studied will be provided by contacting the instructor.

Teaching Soft Skills (91954)
Secondo anno di Global economy and business (LM56), Global Economy and Business
Credits (CFU): 3,00
Program:
The course starts from the distinction between hard skills and soft skills.
Hard skills are specific and teachable. They are actual knowledge, technical or intellectual and are typically quantifiable and measurable. They include traditional knowledge areas such as the STEM subjects  Science, Technology, Engineering and Mathematics  but also encompass other measurable skills such as language proficiency and technical skills.
By contrast, soft skills are more difficult to measure and quantify. Often called interpersonal skills, they include personality traits such as critical thinking, leadership, problemsolving and life skills  which include negotiating, networking, and working with cultural diversity as well as communication and listening, etiquette, getting along with other people.
Both types of skills are necessary to successfully perform and advance in most jobs.
Presentation skills are especially important in the workplace. Knowing how to present your ideas, to a group or an individual, in a way which is both informative and persuasive, is the best tool in your arsenal for success and career advancement.
The course focus on the ability of making a successful presentation.
Reference books:
Attending students
Notes provided by the instructor and additional materials provided to prepare a specific presentation that will be selected based on the background education of students.
Nonattending students
Specific material to be studied will be provided by contacting the instructor.

Teaching Soft Skills (91954)
Secondo anno di Economics and Entrepreneurship (LM56), Curriculum unico
Credits (CFU): 3,00
Program:
The course starts from the distinction between hard skills and soft skills.
Hard skills are specific and teachable. They are actual knowledge, technical or intellectual and are typically quantifiable and measurable. They include traditional knowledge areas such as the STEM subjects  Science, Technology, Engineering and Mathematics  but also encompass other measurable skills such as language proficiency and technical skills.
By contrast, soft skills are more difficult to measure and quantify. Often called interpersonal skills, they include personality traits such as critical thinking, leadership, problemsolving and life skills  which include negotiating, networking, and working with cultural diversity as well as communication and listening, etiquette, getting along with other people.
Both types of skills are necessary to successfully perform and advance in most jobs.
Presentation skills are especially important in the workplace. Knowing how to present your ideas, to a group or an individual, in a way which is both informative and persuasive, is the best tool in your arsenal for success and career advancement.
The course focus on the ability of making a successful presentation.
Reference books:
Attending students
Notes provided by the instructor and additional materials provided to prepare a specific presentation that will be selected based on the background education of students.
Nonattending students
Specific material to be studied will be provided by contacting the instructor.

Teaching Soft Skills (91954)
Secondo anno di Civil and Environmental Engineering (LM23), Civil and Environmental Engineering
Credits (CFU): 3,00
Program:
The course starts from the distinction between hard skills and soft skills.
Hard skills are specific and teachable. They are actual knowledge, technical or intellectual and are typically quantifiable and measurable. They include traditional knowledge areas such as the STEM subjects  Science, Technology, Engineering and Mathematics  but also encompass other measurable skills such as language proficiency and technical skills.
By contrast, soft skills are more difficult to measure and quantify. Often called interpersonal skills, they include personality traits such as critical thinking, leadership, problemsolving and life skills  which include negotiating, networking, and working with cultural diversity as well as communication and listening, etiquette, getting along with other people.
Both types of skills are necessary to successfully perform and advance in most jobs.
Presentation skills are especially important in the workplace. Knowing how to present your ideas, to a group or an individual, in a way which is both informative and persuasive, is the best tool in your arsenal for success and career advancement.
The course focus on the ability of making a successful presentation.
Reference books:
Attending students
Notes provided by the instructor and additional materials provided to prepare a specific presentation that will be selected based on the background education of students.
Nonattending students
Specific material to be studied will be provided by contacting the instructor.

Teaching Matematica finanziaria (91826)
Terzo anno di ECONOMIA AZIENDALE FROSINONE  Piazza Marzi, 1  03100 (L18), Economia e management dell'innovazione
Credits (CFU): 6,00
Program:
Future value. Present value. Interest. Discount. Accumulation function. Discount factor. Effective interest and discount rates. Financial regimes: simple and compound. Nominal interest rate convertible mthly. Force of interest.
Annuities: introduction and classification. Future and present value of annuitiesimmediate, annuitiesdue, perpetuities, annuities payable mthly. Unknown time of an annuity  Unknown rate of interest of an annuity (methods for its approximated calculus). Bond portfolios.
Loan agreement. Term of loan. Outstanding balance. Loan amortization schedules: different repayment schemes.
Bond valuation. Determination of bond price. Amortization of a bond. Callable Bonds: Optional Redemption Dates. Applications.
Measuring the rate of return of an investment. Internal Rate of Return Defined and Net Present Value. Applications.
Market structure: spot and forward prices. Term structures of interest rates.
More advanced financial analysis: yield curves. Duration: definition and properties. Cashflow matching. Volatility. Convexity.
Reference books:
• S.A. Broverman, Matematica finanziaria, Edizione italiana a cura di A. Olivieri e G. Favero, Egea, 2019.