K. Sydsaeter, P. Hammond, A. Strom.
Metodi Matematici per l'Analisi Economica e Finanziaria.
Pearson, 2015.
Learning Objectives
KNOWLEDGE: Elements of mathematical analysis. Differential calculus for functions of a single variable.
COMPETENCE: The course aims at providing students with tools required for building and studying mathematical models that use real functions of one variable, typically found in economic applications. Students will learn the use of calculus for the study of functions and of simple optimization problems.
Prerequisites
The natural numbers. The integers. The rationals. An intuitive idea of real numbers. Arithmetic operations and their properties. Percentages. Prime numbers. Factorization of a natural number. Greatest common divisor and least common multiple. Inequalities and manipulation of inequalities. Absolute value. Powers, roots and their properties. Simplifying expressions.
Polynomials. Special products. How to factor polynomial into irreducible terms in simple cases. Polynomial identity. Ratios of polynomials. Identities and equations. Solutions for an equation. Equations of degree one or degree two. Solutions (roots) of a polynomial. Equations containing ratios of polynomials. Equations with radicals. Inequalities. Solving inequalities of degree one and degree two, inequalities, with ratios of polynomials, with radicals. Summations and Newton's Binomial formula.
Cartesian coordinates in the plane. Pythagorean theorem. Distance between two points. Equation of the line. Linear systems with two equations and two unknowns. Parallel lines and perpendicular lines. Equation of the parabola. Equation of a circle.
Most of these topics are covered in Ch. 0 (paragraphs 0.1 to 0.14 included), in Ch. 1 (paragraphs 1.4 to 1.7 included) and in Ch. 2 (Par. 2.5) of the textbook.
Teaching Methods
Class lectures, seminars, online guided self assessment, weekly homework assignments.
The course length is 12 weeks with two classes a week.
Further information
For more information see the course's moodle page.
Type of Assessment
There is a written exam including 15 multiple choice questions and 2/3 problems.
Course program
1. Introduction
2. Sums, logic, sets
3. Functions, graphs, power functions
4. Exponentials, the log
5. Test on prerequisites
6. Operations between functions
7. Compositions and inverses
8. Slope and derivative
9. Monotonicity and rates of change
10. Limits
11. Rules for taking derivatives
12. Derivative of the composition
13. Higher order derivatives and concavity
14. Derivatives of exponentials and the log
15. Derivative of implicit functions and of the inverse
16. Linear approximation
17. Continuity
18. Limits, intermediate values
19. Hopital rule
20. Maxima, minima and Fermat's Theorem
21. Test to locate max and min
22. Weierstrass and Lagrange
23. Local extreme points
24. Inflection points