Course Unit Page

Teacher Gian Luca Tassinari

Credits 12

SSD SECSS/06

Teaching Mode Traditional lectures

Language English

Campus of Bologna

Degree Programme First cycle degree programme (L) in Business and Economics (cod. 8965)

Course Timetable from Nov 08, 2021 to May 19, 2022
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.
Academic Year 2021/2022
Learning outcomes
At the end of the course the student will be capable of using the techniques of Linear Algebra; furthermore he will have acquired a working knowledge of First Year Calculus, together with the related applications in Finance and Economics.
Course contents
A preliminary tutorial (30 hours) covers a number of introductory topics (socalled precalculus), including elementary set theory, sets of real numbers, complex numbers, polynomials, linear and quadratic equations and inequalities, systems of inequalities, absolute value and rational inequalities, Cartesian coordinate system, basic analytic geometry, basic concepts and definitions about functions, elementary functions (power, exponential and logarithmic), exponential and logarithmic equations and inequalities, trigonometric functions.
PLEASE NOTE: It is of FUNDAMENTAL IMPORTANCE that all students have a perfect knowledge of the topics covered in the introductory mathematics course as:
a) they will not be reexplained in the general mathematics course;
b) without an excellent command of these topics, the possibility of understanding the contents of General Mathematics is nil.
Course content  Calculus and Linear Algebra (90 hours)
Introduction to the course and crash review of preliminary mathematical notions
Onevariable functions: basic definitions, graphs and elementary functions (linear, quadratic, polynomial, rational, irrational, power, exponential, logarithmic, absolute value). Odd and even functions. Composite functions. Inverse functions.
Limits and continuity.
Differentiation of onevariable functions: tangents and derivatives, rules of differentiation, chain rule, higherorder derivatives.
Derivatives in use: implicit differentiation and economic examples, differentiation of the inverse function, linear and quadratic approximations, Taylor's formula, elasticities; continuity and differentiability, intermediatevalue theorem, De L’Hôpital’s Rule.
Singlevariable optimization: local and global extrema, stationary points and firstorder condition, simple tests for extreme points, extreme points for concave and convex functions, secondorder derivative and convexity, inflection points, study of the graph of a function, asymptotes.
Sequences and series; convergence criteria; geometric series; Taylor's series. Sequences and series in financial mathematics.
Difference equations. Linear, first order, autonomous difference equations. Steady state and convergence analysis. Linear, first order, non autonomous, difference equations. Difference equations in financial mathematics.
Integration: the Riemann integral and its geometrical interpretation; primitives and indefinite integrals, fundamental theorems of integral calculus. Rules and methods of integration: immediate integrals, integration of rational functions, integration by parts, integration by substitution. Improper integrals.
Integration in economics: continuous compounding and discounting, present values.Differential equations. First order differential equations. Linear, first order, autonomous differential equations. Steady state and convergence analysis. Linear, first order, nonautonomous differential equations. Differential equations with separable variables. Differencial equations in financial mathematics.
Linear algebra: vector spaces, bases and dimension; matrices and their properties, matrix operations, rank and determinant; linear maps and associated matrices, systems of equations, existence of solutions, cases of one solution and infinitely many solutions, Gaussian elimination, inverse of a matrix and Cramer's rule; eigenvalues and eigenvectors.
Multivariable calculus: partial derivatives with two variables, geometric interpretation; partial elasticities; chain rules, implicit differentiation along a level curve; functions of more variables, gradient, differentials and linear approximations; economic applications.
Multivariable optimization; maxima, minima and saddle points; tests based on second derivatives; constrained optimization and Lagrange multipliers.Readings/Bibliography
R.A. ADAMS, C. ESSEX. Calculus, a complete course, 9th Edition, Pearson, 2018.
Chapters: preliminaries, 1, 2, 3, 4, 5, 6, 7.9, 9, 10, 12, 13
K. SYDSÆTER, P. HAMMOND, A. STRØM, A. CARVAJAL. Essential Mathematics for Economic Analysis, 5th Edition. Pearson, 2016.
Chapters: 1, 2,3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.
Lecture notes on Difference Equations and Eigenvalues and Eigenvectors will be provided by the Professor.
Teaching methods
Class lectures. During the class lectures (as well as in the additional exercise classes) each topic will be illustrated by examples and workedout exercises.
Assessment methods
Written exam: students have to solve different exercises on the course topics. To each exercise a given maximum number of point is associated, and to get it the student has to solve correctly the exercise and all the steps must be justified. The theoretical maximum number of points atteinable in case of a perfect exam is 32.
The test assessment grid will be as follows:
· <18 insufficient
· 1823 sufficient
· 2427 average/good
· 2830 very good
· 30 cum laude excellent/outstanding
If your total is <=30 score, your score corresponds to your mark. If your score is >30, then you get 30 cum laude.
The exam of the first (summer) session can be taken in 3 steps: a first midterm exam (after 1/3 of the course, during the midterm session of January/February) with a duration 1 hour, a second partial exam (after 2/3 of the course, during the session of April) with a duration of 1 hour on the second part the course, and a third midterm exam of duration 1 hour on the third part of the course during the first call of session of June/July. In occasion of the third partial exam, students who have not taken the partials can only take the total exam (duration 3 hours).
NOTE: ALL CLABE STUDENTS ARE ALLOWED TO TAKE MIDTERM EXAMS AND NOT ONLY FIRST YEAR STUDENTS.
During the exam, students are not allowed to use calculators. Textbooks and other teaching materials are not allowed.
NOTE: THOSE WHO COMMIT FRAUD DURING THE EXAM WILL NOT BE ABLE TO TAKE THE EXAM FOR A FULL A.A. UNTIL THE CORRESPONDING CALL OF THE FOLLOWING YEAR AND THE TEST AT THAT POINT WILL BECOME ORAL AND WILL INCLUDE THE SOLUTION OF EXERCISES, THE ENUNCIATION AND DEMONSTRATION OF ALL THEOREMS RELATING TO THE TOPICS SHOWN IN THE COURSE'S PROGRAM AND CONTAINED IN THE BOOKS.
Grade rejection
The only grades that can be rejected without any communication from the student are those of the first and second midterm exams.
Teaching tools
Slides
Blackboard
Office hours
See the website of Gian Luca Tassinari