MATHEMATICS - 2
|Academic year||2019/2020 Syllabus of previous years|
|Official course title||MATHEMATICS - 2|
|Course code||ET2018 (AF:304801 AR:168331)|
|Modality||On campus classes|
|ECTS credits||6 out of 12 of MATHEMATICS|
|Degree level||Bachelor's Degree Programme|
|Educational sector code||SECS-S/06|
|Moodle||Go to Moodle page|
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.
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 be revised by the student, for example, by studying chapters 0, 1 and 2 of the reference textbook and by attending the Additional Learning Requirements of Mathematics courses
(ALR). Some of these topics are also reported in the syllabus of the CISIA tolc-E test for the access to the degree program (see www.cisiaonline.it).
FIRST MODULE (Mathematics 1)
Domain, limits and derivative of single variable functions.
Single variable optimization.
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.
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.
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 a rigorous reasoning, several examples and applications to economics are discussed during the lectures.
Students are also accompanied in carrying out a large number of guided exercises through the use of an online learning platform associated with the textbook in use.
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: firstname.lastname@example.org.