Degree | Type | Year |
---|---|---|
Business Administration and Management | FB | 1 |
Economics | FB | 1 |
You can view this information at the end of this document.
To successfully follow this course, students must be able to handle basic mathematical concepts and tools, as well as have previously acquired fundamental notions of continuity, derivatives, and the analysis and graphical representation of real functions of a single real variable, as presented and studied in the Mathematics I course.
Topic 1. VECTOR AND MATRIX ALGEBRA
1.1. Systems of linear equations
1.2. Operations with matrices and vectors
1.3. Linear dependence and independence of vectors
1.4. Properties of basic operations and geometric interpretations
1.5. Norm and Euclidean distance
1.6. Sets, lines, and planes
Topic 2. MATRIX CALCULUS
2.1. Matrices, determinants, inverse matrices, and rank
2.2. Solving systems of equations using matrices
Topic 3. STUDY OF MULTIVARIABLE FUNCTIONS
3.1. Characteristics of multivariable functions
3.2. Geometric representation
3.3. Surfaces and distances
3.4. Level curves
Topic 4. PARTIAL DERIVATIVES AND DIFFERENTIABLE FUNCTIONS
4.1. Derivative of a function at a point in the direction of a unit vector
4.2. Partial derivatives
4.3. Gradient of a function at a point. Geometric interpretation and directional derivatives
4.4. Differentiable functions. Continuity of partial derivatives
4.5. Chain rule
4.6. Partial derivatives of linear combinations and quadratic forms
4.7. First- and second-order Taylor approximations
Topic 5. IMPLICIT FUNCTION THEOREM AND INVERSE FUNCTION THEOREM
5.1. Implicit function theorem
5.2. Inverse function theorem
5.3. Applications and geometric intuition
Topic 6. UNCONSTRAINED OPTIMIZATION
6.1. Local and global optima
6.2. First- and second-order conditions for local optima
6.3. Global optima of concave and convex functions
Topic 7. CONSTRAINED OPTIMIZATION
7.1. Maximization and minimization problems with equality constraints
7.2. Constrained local optima. Lagrange’s Theorem
7.3. Global constrained optima of concave and convex functions
7.4. Weierstrass Theorem
7.5. Introduction to inequality constraints
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Preparation and solution of exercises | 17 | 0.68 | CM01, CM02, CM04, CM20, CM21, CM23, KM02, KM19, SM01, SM02, SM03, SM21, SM22, CM01 |
Theory classes | 32.5 | 1.3 | CM01, CM02, CM20, SM01, SM02, SM03, SM21, SM22, CM01 |
Type: Supervised | |||
Progress monitoring | 3 | 0.12 | CM01, CM02, CM04, CM20, CM21, CM23, KM02, KM19, SM01, SM02, SM03, SM21, SM22, CM01 |
Tutorials | 7 | 0.28 | CM01, CM02, CM04, CM20, CM21, CM23, KM02, KM19, SM01, SM02, SM03, SM21, SM22, CM01 |
Type: Autonomous | |||
Exercise preparation and problem-solving | 40 | 1.6 | |
Study | 45 | 1.8 | CM01, CM02, CM04, CM20, CM21, CM23, KM02, KM19, SM01, SM02, SM03, SM21, SM22, CM01 |
The aim of this activity is to introduce fundamental notions and facilitate student learning, with an emphasis on the economic applications of the mathematical concepts studied.
The goal of this activity is to foster student independence in the learning process by applying theoretical concepts to families of multivariable functions.
Each topic will be accompanied by a list of problems that students must solve independently. This activity has a dual purpose: on one hand, to help students assimilate the theoretical concepts presented in class; on the other hand, to develop the necessary problem-solving skills.
Collaborative problem solving will be encouraged, through stable work groups of 3 or 4 students throughout the semester, who will collaborate to overcome difficulties encountered by any of the group members.
This activity aims to address and clarify doubts that students may have had while working on the problem sets, allowing them to better understand the material and correct any mistakes made.
Students will have access to a number of scheduled hours during which professors will be available to answer questions in person.
The proposed teaching methodology may be subject to change depending on any restrictions on in-person attendance imposed by health authorities.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Deliverables and continuous assessment | 20% | 2 | 0.08 | CM01, CM02, CM04, CM20, CM21, CM23, KM02, KM19, SM01, SM02, SM03, SM21, SM22 |
Final exam | 50% | 2 | 0.08 | CM01, CM02, CM04, CM20, CM21, KM02, KM19, SM01, SM02, SM03, SM21, SM22 |
Parcial exam | 30% | 1.5 | 0.06 | CM01, CM02, CM04, CM20, CM21, KM02, KM19, SM01, SM02, SM03, SM21, SM22 |
The midterm exam will account for 30% of the final average grade of the course.
The final exam will account for 50% of the final average grade of the course.
Thus, the final average grade is calculated as follows:
Final average grade =
30% (midterm exam grade) +
50% (final exam grade) +
20% (grade from exercises/assignments/laboratory tests)
The course will be considered passed if the following two requirements are met:
The final average grade is equal to or greater than 5, and
The final exam grade is equal to or greater than 3.
If a student meets the first requirement but not the second, they will receive a final average grade of 4.5 and may take the reassessment exam, according to the conditions outlined in the “Reassessment Process” section below.
If a student meets the second requirement but not the first, or neither of the two, they may still take the reassessment exam, under the same conditions.
A student who has not participated in any assessment activity will be considered "Not assessable."
The dates of the various assessment activities (midterm exams, in-class exercises, assignment submissions, etc.) will be announced well in advance during the semester.
The date of the final exam is scheduled in the Faculty’s official exam calendar.
“Assessment activities may not be rescheduled, except in cases of exceptional and duly justified reasons that prevent the student from attending an evaluation activity.
In such cases, the academic program coordinators, after consultation with the teaching staff and affectedstudents, will propose a new schedule within the corresponding academic period.”
(Section 1, Article 264 – Assessment Activities Calendar, UAB Academic Regulations)
Students from the Faculty of Economics and Business who, according to the above, need to reschedule an assessment must submit a request by filling out the form:
Assessment Rescheduling Request: e-Form for Rescheduling Assessments.
Coinciding with the final exam, the date and method of publication of the final grades will be announced.
Details regarding the procedure, location, date, and time of the exam review session will also be provided, in accordance with university regulations.
“To participate in the reassessment process, students must have been previously assessed in activities representing at least two-thirds of the total grade for the course or module.”
(Section 2, Article 261 – Reassessment, UAB Academic Regulations)
Students must have obtained a final average grade between 3.5 and 4.9.
The date of the reassessment exam will be scheduled in the Faculty’s exam calendar.
If the student passes this exam, they will pass the course with a grade of 5. Otherwise, their original grade will remain unchanged.
Without prejudice to other disciplinary measures deemed appropriate and in accordance with current academic regulations:
“If a student commits any irregularity that could lead to a significant alteration of the grade of an assessment activity, that activity will be graded with a 0, regardless of any disciplinary proceedings that may be initiated.
If multiple irregularities occur across different assessment activities in the same course, the final grade for that course will be 0.”
(Section 11, Article 266 – Assessment Results, UAB Academic Regulations)
Sydsaeter, K., P.J. Hammond, and A. Carvajal, 2012, Matemáticas para el Análisis Económico. Prentice Hall, Madrid.
(Available online through the UAB library)
This is a widely accepted reference manual with a long-standing reputation. Thanks to its updated editions, it has become a standard reference work. It also covers the syllabus of the course Mathematics for Economists I. It is a comprehensive and accessible textbook focused on economic applications.
The same authors have another book at a slightly more basic level, available only in English, which is also a good option as a main textbook:
Sydsaeter, K. and P.J. Hammond, 2012, Essential Mathematics for Economic Analysis. Fourth edition. Pearson Education.
The following manuals can be very useful for students, whether to complement the content of the main textbook or to expand their knowledge:
Alegre, P., L. Jorba, F.J. Orti, G. Rodríguez, J.B. Sáez, T. Sancho, and A. Terceño, 2000, Solved Exercises in Business Mathematics II. Editorial Alfacentauro, Madrid.
Besada, M., F.J. García, M.A. Mirás, and M.C. Vázquez, 2001, Multivariable Calculus: Questions and Solved Exercises. Prentice Hall, Madrid.
Chiang, A.C., 2006, Fundamental Methods of Mathematical Economics. McGraw-Hill, Madrid.
Larson, R., R. Hostetler, and B. Edwards, 2006, Calculus II of Several Variables. McGraw-Hill, Mexico.
Additional material will be uploaded to the course webpage on the Virtual Campus, at the discretion of the teaching staff.
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Please note that this information is provisional until 30 November 2025. You can check it through this link. To consult the language you will need to enter the CODE of the subject.
Name | Group | Language | Semester | Turn |
---|---|---|---|---|
(PAUL) Classroom practices | 1 | Spanish | second semester | morning-mixed |
(PAUL) Classroom practices | 2 | Catalan | second semester | morning-mixed |
(PAUL) Classroom practices | 4 | English | second semester | morning-mixed |
(PAUL) Classroom practices | 8 | English | second semester | morning-mixed |
(PAUL) Classroom practices | 51 | Spanish | second semester | afternoon |
(PAUL) Classroom practices | 52 | Catalan | second semester | afternoon |
(PAUL) Classroom practices | 60 | Spanish | second semester | morning-mixed |
(TE) Theory | 1 | Spanish | second semester | morning-mixed |
(TE) Theory | 2 | Catalan | second semester | morning-mixed |
(TE) Theory | 4 | English | second semester | morning-mixed |
(TE) Theory | 8 | English | second semester | morning-mixed |
(TE) Theory | 51 | Catalan | second semester | afternoon |
(TE) Theory | 52 | Catalan | second semester | afternoon |
(TE) Theory | 60 | Spanish | second semester | morning-mixed |