MATHEMATICS - 2

The Mathematics course is a compulsory course for all students. It is the first course in the quantitative area: it takes place in the first two periods of the first year of the course of study, the first module (Mathematics 1) in the first period and the second module (Mathematics 2) in the second period. The aim is to provide a common language of a logical-mathematical type as well as the essential notions of calculus, financial mathematics, and linear algebra. These contents are analytical tools necessary to face the theoretical contents and to solve the managerial problems that are proposed in the following courses of business administration, economics, and quantitative aspects of the course study.

At the end of “Mathematics I” students should have acquired the fundamentals of calculus in one variable. Specifically, students should have acquired the following skills.

a) Knowledge and understanding
a.1) Knowledge of basic definitions in calculus in one variable, such as: derivatives, limits, integrals;
a.2) Interpretation of the above definitions in terms of geometric properties, supported by a span of crucial examples.

b) Ability to apply knowledge and understanding
b.1) Ability to compute, for functions of one variable: derivatives, limits, integrals (elementary, by parts, by substitution);
b.2) Ability to analyse properties of functions of one variable, such as monotonicity, convexity, behaviour in the long run;
b.3) Ability to compute stationary and inflection points; ability to maximize/minimize a quantity described by a one variable function, particularly when it describes an economic variable;
b.3) Ability to interpret all above properties in economic/managerial examples.

c) (Lifelong) learning skills
c.1) Improved ability to handle a formal language, to make logic deductions; enhance rigorous rational thinking;
c.2) Improved ability to translate a problem into formal terms, solve it and interpret the solution in terms of the original problem.

Students must be clear of didactic debts (Additional Learning Requirements, ALR).

Topics usually taught in undergraduate courses are assumed to be well known, in particular: set theory notation, real numbers; algebraic rules; fractions; powers; inequalities; absolute value; single variable elementary functions, linear, power, exponential, logarithmic and their graphs; graphs obtained by translation from graphs of elementary functions; equations and inequalities (also parametric), first and second degree, fractional, exponential and logarithmic; analytical geometry: cartesian coordinates, distance between two points, equation of a straight line, parabola and circumference and their graphic representation; symbol of summation.
These topics can also be revised by the student, for example, by studying chapters 0, 1, and 2 of the reference textbook and by attending the ALR class.

The program of the whole course (12 cfu, 60 hours of lectures) is the following:

FIRST MODULE (Mathematics 1)
Domain, limits and derivative of single variable functions.
Single variable optimization.
Integrals.
Present and future values in financial mathematics, streams of cash flow.

SECOND MODULE (Mathematics 2)
Functions of several variables.
Unconstrained and constrained optimization with several variables.
Matrix algebra and linear equations systems.

K. Sydsaeter, P. Hammond and A. Strom, Essential Mathematics for Economic Analysis (Fifth Edition), Pearson, 2016.

ISBN:
978-1-292-07461-0 (print);
978-1-292-07465-8 (pdf);
978-1-292-07470-2 (epub).

Grading is based on a final written exam, including all topics taught in Mathematics 1 and Mathematics 2, and an optional oral exam.
The written exam consists of 4-10 problems, on the topics of both Mathematics 1 and Mathematics 2. The abilities acquired by the students are verified by requiring them to solve the problems. Their acquired knowledge is verified by asking them to justify their answers, on the basis of the theoretical results (definitions and theorems) presented and practiced in class.

In the written exam only the use of your pen is allowed, instead electronic tools, notes or books are not allowed.
Registration for the written tests is mandatory.

Two partial exams are issued during the course time span, one covering the topics of Mathematics 1 and one covering those of Mathematics 2. Undergoing both partial exams is considered equivalent to undergo the final written exam, with overall grade equal to the sum of the grades in the partials.

In the two periods of teaching activity, the course consists of 30 + 30 hours of face-to-face lectures (unless the Ministry and/or the University dispose otherwise) during which the teacher describes the topics of the course, proposes, analyzes and solves examples and exercises. Other 10 + 10 hours are held by a teaching assistant proposing further exercises in the two modules.
The students in their individual work are required to understand and assimilate the basic concepts of the theory, comparing the personal notes of the course with the recommended texts, so as to be able to face and identify the solution of exercises and problems.
In order to develop language precision and rigorous reasoning, several examples and applications to economics are discussed during the lectures.

Detailed information on the program and study materials will be communicated at the beginning of the course on the e-learning page of the course (moodle.unive.it).

Accessibility, Disability and Inclusion
Accommodation and support services for students with disabilities and students with specific learning impairments
Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding support
services and accommodation available to students with disabilities. This includes students with
mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). If you have a disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.

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