K. Sydsaeter, P. Hammond, A. Strom. Metodi Matematici per l'Analisi Economica e Finanziaria. Pearson, 2015.
Learning Objectives
The goal of the course is to provide mathematical tools that allow to build and understand simple economic models that use functions of one real variable. At the end of the course the student will have to know the mathematical concepts and the theorems presented. With regard to these concepts and theorems, the student will also need to be able to understand and appropriately use the formalism and the syntax and solve exercises and problems.
Prerequisites
Basic set theory. Natural numbers, whole numbers and rational numbers. Prime numbers. Factorization of a natural number. Greatest common divisor and least common multiple. Percentages. Real numbers (intuitive idea). Absolute value. Powers and roots. Polynomials. Sum and product of polynomials. Square and cube of a binomial. Notable products. Factorization of simple polynomials. Rational expressions. Sum and product of rational expressions. Identities. Equations and solutions of an equation. Inequalities and solutions of an inequality. First and second degree equations and inequalities. Equations and inequalities of a higher degree. Equations and inequalities with rational expressions. Irrational equations and inequalities. Systems of equations and systems of inequalities. Cartesian coordinates in the plane. Pythagorean theorem. Distance between two points. Equation of the straight line. Linear systems of two equations in two unknowns. Parallelism and perpendicularity of two lines. Equation of the parabola. Circumference equation.
Teaching Methods
Class lectures. The course length is 12 weeks with two classes a week.
Further information
The course has an internet page on the platform Moodle, which provides further information on the course.
Type of Assessment
The learning assessment takes place through a written test. The written test is aimed to verify:
-the knowledge acquired regarding the mathematical concepts and theorems presented during the course,
-the understanding and use of the formalism and the syntax related to the concepts studied,
-the ability to apply the acquired knowledge to solve exercises and problems.
The written test has a duration of 90 minutes and includes:
- exercises aimed to verify the knowledge of the concepts and theorems presented during the course.
- exercises aimed to verify the ability to apply the knowledge acquired.
If the student gets a failing grade (smaller than 18) in the written test, then the student fails the exam.
If the student gets a passing grade (greater or equal than 18) in the written test, then the student may request, at his own discretion, to take an oral test. If the student does not take the oral test the final grade will coincide with the grade obtained in the written test. If the student takes the oral test the final grade is determined on the basis of the grade of the written test and the evaluation of the oral test. To achieve the "30 cum laude" grade it is necessary for the student to take the oral test.
If the student gets a passing grade (greater or equal than 18) in the written test, instructors may reserve the right to integrate the written exam with the oral test in order to better assess the preparation of the student or in case of apparent non-compliance with the rules of good conduct by the student during the written exam. Also in this case the final grade is determined on the basis of the grade of the written test and the evaluation of the oral test.
Course program
Basic set theory. Real numbers, intervals, and absolute value. Functions of one variable. Graph of a function. Elementary functions: linear, quadratic, polynomial, exponential, logarithm, power functions. Operations between functions. Composition of functions. Monotonic functions. Inverse functions. Global maximum and minimum points of a function. Limits of a function. Methods for limits calculation. Continuous functions. Theorems on continuous functions. Derivative of a function. Tangent line to the graph of a function. Derivative rules for the sum, the product, the quotient and the composition of functions. Derivatives as a tool to study of the monotonicity of a function. Derivative of exponential and logarithmic functions. Higher-orders derivatives. Concave and convex functions. Linear and quadratic approximation. Implicit differentiation. De l’Hopital’s rule. Single-variable optimization. Stationary points. Local extreme points. Necessary first order conditions for extreme points. Sufficient first order conditions for extreme points. Searching for extreme values in bounded and closed intervals. General method for studying a function.