Course code: 176104 | Subject title: MATHEMATICS | ||||
Credits: 6 | Type of subject: Basic | Year: 1 | Period: 1º S | ||
Department: Mathematics | |||||
Lecturers: | |||||
INDURAIN ERASO, ESTEBAN [Mentoring ] |
Differential calculus: a study of the functions of one and several variables, properties, operations, graphical representations, continuity, differentiability, asymptotic behavior. Homogeneous functions. Optimization, extreme of functions of one and several variables, unconstrained optimization, optimization with equality constraints. Integral calculus: indefinite and definite integral. Calculation of primitives. Applications to the calculation of areas and other applications. Matrices, determinants, operations and applications: Matrix calculus. Discussion and solving of systems of linear equations. Applications to Economics and Business Models.
The methodology used throughout this subject matter aims to give a positive answer to the following challenges (among others):
To do so, the lecturer will develop the scheduled activities in the following way:
(1) Theoretical classes (that will include exercises) will be taught in the lecture room by the lecturer in charge of this subject matter. Along these lectures, the lecturer will introduce and develop the most important facts, enlighting them by means of the inclusion of a wide list of examples and practical cases to be analyzed. Therefore, the applications are understood as a base and ground on which the theory leans, and not only as a mere list of exercises. The exposition made by the lecturer will show the main lines and aspects of the subject matter. The complementary use of the bibliography, access to the Internet, or use of the tutorials and consulting hours to complete, improve and reinforce the items shown in the lecture room, is a task to be done by the students.
(2) Practical and problem-solving sessions, in which the lecturer will state and help the students to solve (in the lecture room) typical problems related to the subject matter. To do so, the lecturer will select, when available, ``case studies", that is: key problems that perhaps are not trivial or straightforward, and have some special difficulty. These problems should show in a clear way how the most important theoretical facts interact to get a solution, output or result. These kinds of lectures will require an active (and compulsory) participation of the students that should have tried to solve (in advance) the problems stated. Having this in mind, it is very important here that the students work in teams in which they will comment, discuss, analyze, get solutions and draw conclusions from the problems they solve.
(3) The personal work of the student is crucial here, since the subject is exigent and forces the student to update, at the same speed in which it is taught, the amount of matter shown in the lecture room. To cope with this, the student must develop techniques of self-training. To control all this process, the interaction student-lecturer through tutorials and consulting hours is compulsory.
(4) The student must get used to working in teams as a complement to his/her individual process of learning. Having this in mind, the lecture should also provide the students with sessions of "group-tutorials", in which a team of students will expose the achievements obtained (working in group) on schemes and models to be analyzed and discussed.
(5) Systematic ``control tests" should be scheduled by the lecturer to be done in the lecture room by the students in a period of, say, once a forthnight, to have a clear idea about how the students are understanding and using the main concepts and ideas. This is a way to control the ``continuity” in the way in which the students interact with the subject matter. Notice that to assimilate the main ideas of Mathematics, a process of continuous learning is required.
1. MATRIX CALCULUS (LINEAR ALGEBRA)
1.1. Matrices
1.2. Transpose of a matrix
1.3. Addition of matrices.
1.4. Product of a matrix by a scalar number.
1.5. Product of matrices.
1.6. Inverse matrices.
1.7. Elementary transformations of a matrix.
1.8. Successive powers of a matrix.
1.9. Determinants
1.10. Determinants and inverse matrices.
1.11. Rank of a matrix.
1.12. Systems of linear equations.
2. DIFFERENTIAL CALCULUS
2.1. The real line and the n-dimensional space.
2.2. Real functions.
2.3. Limits.
2.4. Continuity.
2.5. Derivatives (functions of a single real variable).
2.6. Partial derivatives (functions of several real variables).
2.7. Optimization (functions of a single real variable).
2.8. Concave and convex functions.
2.9. Optimization without constraints (functions of two real variables).
2.10. Optimization with constraints.
3. INTEGRAL CALCULUS
3.1. Primitive integral of a real function.
3.2. Definite integral.
4: APPENDICES
4.1. Homogeneous functions.
4.2 Optimization theory (functions of several real variables).
Access the bibliography that your professor has requested from the Library.
By means of the tool “MiAulario”, the students will have access to schemes, lists of exercises, links to complementary material, etc., related to the subject matter.
We do not recommend any particular textbook on this subject. There are many possible books on Differential Calculus, Integral Calculus, Linear Algebra and related items, even from a point of view of Economics or reportedly addressed to students of Economics and/or Business Administration, that can be found in any "average-size" universitary library.
Perhaps the reference "Mathematical models in the Social, Management ald Life Sciences" , by D.N. Burghes and A. D. Wood (Ellis Horwood. Chichester, UK. 1984) is an excellent reference to find "case-studies" related to the main concepts to be developed throughout the semester in this subject matter.
For the sake of completeness, we include below a list (not exhaustive, and by no means the only possible one) of texts in Spanish that can be used in the preparation of some lectures.
LIST (texts in Spanish) FOLLOWS: