Curs 2009-2010

Mathematics 2 (21124)

(Versió en català)

• Name of course: Mathematics 2
• Academic year: 2009-10          Study year: 1st         Trimester: 2nd
•  Degree: IBE                             Corse code:       
•  Nunmber of ECTS credits: 5   Hours of dedication by student: 125
•  Language of instruction: English
•  Professors: Bernat Anton, Angel Gil, Michael Greenacre, Alfonso Iodice, Joan Baptista Pallares, Ivan Torrecilla

1.     Presentation of the course

Mathematics 2 is the second in a sequence of three mathematics courses to be taken during the first year of studies in economics and business. Having been introduced to mathematical calculus in Mathematics 1 as well as the basic concepts of optimization of a function of a single variable, students will now extend these ideas to functions of two variables.  The particular properties of two-variable functions will be treated, as well as the theory and practice of finding their optimum values, either maxima or minima as the case may be.  Furthermore, optimization of such functions with equality or inequality constraints is treated.  Thus, this course provides the basic mathematical tools for obtaining optimal values of economic functions, which is a fundamental objective in economics and business practice and research.

2. Competencies to be acquired

 

General Competencies	Specific Competencies
Instrumental 1.   Ability to analyze and synthesize 2.  Ability to organize and plan 3.  General basic knowledge 4.  Problem solving 5.  Written and spoken capabilities Interpersonal 6.  Criticism. Systemic 7.  Research abilities 8.  Learning capacities 9.  Autonomous work   10. Ability to generate new ideas (creativity) Other   11. Written and oral communication skills	1. Knowledge and applications of basic tools in mathematical analysis and linear algebra. 2. Problem formalization for different economics and business contexts through mathematical language. 3. Solutions of optimization problems for functions of two variables.

 

 

3.  Content

-          Block 1: Functions of two variables

-          Block 2: Implicit functions

-          Block 3: Unconstrained optimization of two-variable functions

-          Block 4: Optimization with equality constraints

-          Block 5: Optimization with inequality constraints: linear programming

-          Block 6: Optimization with inequality constraints: nonlinear programming

4.  Evaluation

The grading is based on the following three aspects, of which the first two are for the seminars (counting 50% of the final grade), and the third the final examination (counting 50% of the final grade).

- Tests to be taken during seminars 3, 5 and 7.  Three tests will be conducted during the course, with a duration of 30 minutes. They will consist of problems of the same kind as the ones studied during the two weeks prior to the seminar.  Each test will count 10% of the final grading, that is a total of 32%.

- Grading associated with participation in all 8 seminars and the 8 homeworks delivered at these seminars.   Participation in the seminars will count 10% and the individual homeworks count towards 10% of the final grade. 

- Final Examination. It is a comprehensive examination on all theoretical and practical aspects seen along the course. It counts 50% of the final grade.  In order to pass the course, a minimum of 4/10 (i.e., 20/50) in this exam is required.

- The passing grade for this course is 50% overall, with the condition that at least 20/50 is obtained in the final examination.  The seminar work and the final examination are equally weighted.

For the extraordinary September examination, grading will be computed as 70% for the September examination and 30% for the tests, seminar participation and homework grading obtained during the course, again with a 50% overall grade as a pass and with the condition that at least a 4/10 grade is obtained for the exam (i.e., 28/70 in this case).  Thus the September examination counts more than the seminar work done originally.

5. Bibliography and teaching resources

·         Text book

SYDSAETER, K.; HAMMOND, P. J. Mathematics for Economic Analysis. Englewood Cliffs, N.J. : Prentice Hall, cop. 1995.

·         Other references

TAN, S. T. Matemáticas para Administración y Economía. International Thomson, 1998.

·         Computer software

Students will be introduced to the free R package for drawing two-variable functions in three dimensions.

·         SIREMA

For some classes, web links will be provided to sets of slides in the SIREMA project  - these further reinforce the concepts and tools presented in the theory classes.

6. Methodology

Students are supposed to do the following weekly assignments:

- Individual reading of the scripts before the theoretical sessions

- Attending theoretical sessions

- Personal study, solving homework problems, careful reading of the text book

- Bringing completed homeworks to seminars

- Attending seminars and being prepared to present the solutions of the homework problems, or similar problems, to the class

7.  Activities timetable

Except for the two first weeks when there will be no seminars, activities will be as follows:

Week	In class activities	Out of class activities
Week X	Session 1: Theory (whole group)  Session 2: Theory (whole group)  Session 3: Seminars for solving problems (subgroups) - in three of these seminars 30-minute tests will be conducted which count towards the final grade.	-  Individual reading of the scripts before the theoretical sessions -  Personal study, solving homework problems, careful reading of the text book.

A more detailed description of the contents of each session can be found in aula global as the course progresses.