Download Business Quantitative Methods and Calculations (International

Calculus
GR. A-B: PROF. ANNA TORRIERO; GR. C-DE: PROF.ROSA ALBANESE ; GR. DI-LA: PROF.
MONICA BIANCHI; GR. LE-O: PROF. ENRICO MIGLIERINA; GR. P-SA: PROF. ALVISE MERINI ;
GR. SB-Z: PROF. SALVATORE VASSALLO
COURSE AIMS
The course has two objectives: to present several fundamental mathematical tools
for dealing with economic-financial problems, and to help students to acquire a
precise and essential language. The course will emphasize how to develop a view
toward critically re-examining mathematical concepts which students will find in
their academic pursuits, and how to stimulate the capacity to use mathematical
methods, tools and models in a wide array of applications. The course will cover
basic topics in linear algebra, differential and integral calculus, and optimization;
taken together, these concepts will prove an effective tool for analysing economic
and business phenomena.
COURSE CONTENT
BASIC KNOWLEDGE (pre-course class)
Natural, integer, rational and real numbers. Fundamentals of logic and basic set
theory. Elementary algebra, arithmetic, analytical geometry, trigonometry.
REAL FUNCTIONS OF ONE VARIABLE
− Introductory concepts: Domain. Maximum, minimum, upper and lower bounds.
Bounded functions, monotonic functions, composition of functions, inverse
function. Convex functions.
− Limits and continuity: Limits and related theorems. Operations on limits and
indecision forms. Continuity of functions and related theorems. Asymptotes.
− Differential calculus: Incremental ratio and derivative. Differentiable functions.
Rules of differentiation. Derivative of composite and inverse functions.
Differential calculus fundamental theorems. Global and local maxima and
minima, points of inflexion. Necessary and/or sufficient conditions for the
existence of maxima and minima. Concavity, convexity.
− Integral Calculus: The Riemann (definite) integral. The Mean value theorem.
The Torricelli-Barrow theorem. The indefinite integral. Some techniques of
integration.
ELEMENTS OF LINEAR ALGEBRA
Vectors and matrices and corresponding operations. Determinants. Inverse matrix.
Matrix rank. Systems of linear equations. Rouchè-Capelli theorem, Cramer’s rule.
REAL FUNCTION OF TWO REAL VARIABLES
The euclidean space R2. Domain. Level sets. Partial derivatives. Global and local
maxima and minima. Saddle points. Unconstrained optimization: first and second
order conditions. Constrained optimization via the level set approach and the
Lagrange multiplier method.
READING LIST
L. SCAGLIANTI-A.TORRIERO, Manuale di Matematica, III edition, Cedam, 2009.
M. SCOVENNA-R.GRASSI, Esercizi di Matematica, III edition, Cedam, 2010.
M.BIANCHI-L. SCAGLIANTI, Precorso di Matematica, II edition, Cedam, 2010.
F. BREGA-G. MESSINEO, Esercizi di Matematica generale, Voll. I (2006) e II (2008), Giappicchelli.
Online instructional material is available on Blackboard.
TEACHING METHOD
Lectures (course and pre-course classes), assignments.
ASSESSMENT METHOD
Grading will be based on a written exam in which students will be required to answer
theoretical and practical questions. The oral exam is optional for students having achieved a
grade of 18/30 or higher on the written test, whereas it has to be taken by students with a
grade on the written test of 15/30, 16/30 or 17/30 and also in other cases as specified in
Blackboard. The oral exam concerns all the programme and some simple proofs can be
asked in addition to the proofs of the following theorems: Uniqueness of limits, Sign
preservation, Continuity of a differentiable function, Fermat’s theorem, Rolle’s Theorem,
Mean value theorem, Mean value theorem for integral calculus, Fundamental theorem of
integral calculus.
For all students it is possible to take two partial tests (one during the class period and
the other at the end) as an alternative to the written exam. More detailed information on the
partial tests will be available on Blackboard.
NOTES
Further information can be found on the lecturer's webpage
http://www2.unicatt.it/unicattolica/docenti/index.html or on the Faculty notice board.
at
Basic knowledge will be included in the exam, and thus attendance at the pre-course
classes is highly recommended. More detailed information on the pre-course will be
available on Blackboard. An on line pre-course Teorema is also accessible to the address
http://teorema.cilea.it.