Mathematics II (21124)

Degree/study: degree in International Business Economics
Year: 1st
Term: 2nd
Number of ECTS credits: 5 credits
Hours of studi dedication: 125 hours
Teaching language or languages: English
Teaching Staff: Pelegrí Viader

1. Presentation of the subject

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. Competences to be attained

General Competences	Specific Competences
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. Contents

Block 1: Vectors, lines and planes in 3D-space. Functions of two variables

Block 2: Implicit functions

Block 3: Unconstrained optimization of two-variable functions

Block 4: Global optimization

Block 5: Optimization with inequality constraints

Block 6: Optimization with inequality constraints: linear programming

4. Assessment

The grading is based on the following three aspects, of which the first two are for the seminars (counting 40% of the final grade), and the third the final examination (counting 60% of the final grade). 

- Tests to be taken during seminars 3, 6 and 8.  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 8% of the final grading, that is a total of 24%. 

- Grading associated with participation in all 8 seminars and the 8 homework lists delivered at these seminars.   Participation in the seminars will count 8% and the individual homework and attendance count towards 8% of the final grade.  All in all a 16% of the final grade. 

- Final Examination. It is a comprehensive examination on all theoretical and practical aspects seen along the course. It counts 60% of the final grade.  In order to pass the course, a minimum of 4/10  in this exam is required. 

- The passing grade for this course is 50% overall, with the condition that at least 4/10 is obtained in the final examination. 

- For the extraordinary September examination, grading will be computed as 80% for the September examination and 20% 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.

5. Bibliography and teaching resources

5.1. Basic bibliography

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

5.2. Complementary bibliography

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

5.3. Teaching resources

• Computer software 

Students will be introduced to free software for drawing two-variable functions in three dimensions and the use of a worksheet to solve optimization problems.

• 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 or textbook sections before the theoretical sessions

- Attending theoretical sessions

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

- Bringing completed homework to seminars

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

7. Planning of activities

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/book sections  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.