1. General information
Course:
ADVANCED MATHEMATICS
Code:
56311
Type:
BASIC
ECTS credits:
6
Degree:
418 - UNDERGRAD. IN INDUSTRIAL ELECTRONICS AND AUTOMAT. ENGINEERING
Academic year:
2023-24
Center:
303 - E.DE INGENIERÍA INDUSTRIAL Y AEROESPOACIAL DE TOLEDO
Group(s):
41
Year:
2
Duration:
First semester
Main language:
Spanish
Second language:
Use of additional languages:
English Friendly:
Y
Web site:
Bilingual:
N
Lecturer:
MARIA FUENSANTA ANDRES ABELLAN
- Group(s):
41
Building/Office
Department
Phone number
Email
Office hours
Edificio Sabatini / 1.48
MATEMÁTICAS
926051536
fuensanta.andres@uclm.es
Lecturer:
DAMIAN CASTAÑO TORRIJOS
- Group(s):
41
Building/Office
Department
Phone number
Email
Office hours
Edificio Sabatini / 1.53
MATEMÁTICAS
926051463
Damian.Castano@uclm.es
Lecturer:
JESÚS CASTELLANOS PARRA
- Group(s):
41
Building/Office
Department
Phone number
Email
Office hours
Edificio Sabatini / 1.55
MATEMÁTICAS
926051598
Jesus.Castellanos@uclm.es
Lecturer:
JESUS ROSADO LINARES
- Group(s):
41
Building/Office
Department
Phone number
Email
Office hours
Edificio Sabatini / 1.53
MATEMÁTICAS
926051603
Jesus.Rosado@uclm.es
Lecturer:
DAVID RUIZ GRACIA
- Group(s):
41
Building/Office
Department
Phone number
Email
Office hours
Edificio Sabatini / 1.53
MATEMÁTICAS
926051469
David.Ruiz@uclm.es
2. Pre-Requisites
In order to achieve the learning goals described in section 5, the student must posses all the knowledge and skills associated to the mathematics curricula in earlier stages. In particular, we assume:
- Basic geometry and trigonometry knowledge.
- The ability to perform with ease basic math operations, such as powers, logarithms and fractions.
- The ability to work with polynomials.
- Proficience with computers at a user level.
In addition to this, "Advanced Mathematics" builds on the knowledge and skills acquiered in "Algebra", "Calculus I" and "Calculus II". Even if it is not compulsory to have passed all these subjects to take this course, in that case the learning experiece would become much harder and therefore we strongly recommend not to do so.
3. Justification in the curriculum, relation to other subjects and to the profession
The industrial engineer makes use of physics, mathematics and statistics, together with engineering skills, to develop their profession in aspects such as control, instrumentation and automatization of processes and equipment or the design, manufacturing and operation of industrial products. In these course, the student will further their formation in mathemtics and get a broader perspective and a better understanding of how the knowledge and skills acquiered through the mathematics secquence intertwines with the rest of the degree.
4. Degree competences achieved in this course
| Course competences | |
|---|---|
| Code | Description |
| CB02 | Apply their knowledge to their job or vocation in a professional manner and show that they have the competences to construct and justify arguments and solve problems within their subject area. |
| CB03 | Be able to gather and process relevant information (usually within their subject area) to give opinions, including reflections on relevant social, scientific or ethical issues. |
| CB04 | Transmit information, ideas, problems and solutions for both specialist and non-specialist audiences. |
| CB05 | Have developed the necessary learning abilities to carry on studying autonomously |
| CEB01 | Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge of linear algebra; geometry, differential geometry, differential and partial differential equations, numerical methods, numerical algorithms, statistics and optimisation. |
| CG03 | Knowledge of basic and technological subjects to facilitate learning of new methods and theories, and provide versatility to adapt to new situations. |
| CG04 | Ability to solve problems with initiative, decision-making, creativity, critical reasoning and to communicate and transmit knowledge, skills and abilities in the field of industrial engineering. |
| CT02 | Knowledge and application of information and communication technology. |
| CT03 | Ability to communicate correctly in both spoken and written form. |
5. Objectives or Learning Outcomes
| Course learning outcomes | |
|---|---|
| Description | |
| Ability to approximate functions and data by means of power series and de Fourier developments and their applications. | |
| Ability to express oneself correctly orally and in writing and, in particular ability to use the language of mathematics as a way of accurately expressing the quantities and operations that appear in industrial engineering. Acquired habits of working in a team and behaving respectfully. | |
| Ability to describe processes related to industrial engineering subjects by means of ordinary differential equations and partial differential equations, solve them and interpret the results. | |
| Additional outcomes | |
| Not established. |
6. Units / Contents
-
Unit 1: Ordinary Differential Equations
-
Unit 2: Systems of Ordinary Differential Equations
-
Unit 3: Introduction to numerical methods for Ordinary Differential Equations
-
Unit 4: Integral transforms
-
Unit 5: Functional series and Fourier series.
-
Unit 6: Partial Differential Equations
7. Activities, Units/Modules and Methodology
| Training Activity | Methodology | Related Competences (only degrees before RD 822/2021) | ECTS | Hours | As | Com | Description | |
| Class Attendance (theory) [ON-SITE] | Combination of methods | CEB01 CG03 CT03 | 1.2 | 30 | N | N | The lecturer will teach the theory relative to each unit, present examples and solve model exercieses, so that the student can later work on its own. | |
| Problem solving and/or case studies [ON-SITE] | Combination of methods | CEB01 CG04 CT03 | 0.6 | 15 | N | N | Some lectures will be dedicated to solving exercieses. Some will be solved completely, for some, the lecturer will provide hints so that the student can finish them in their own. This lectures will also serve to solve problems that the students may have encountered while studying and solving excercises on their own. | |
| Class Attendance (practical) [ON-SITE] | Practical or hands-on activities | CEB01 CG03 CG04 CT02 CT03 | 0.4 | 10 | N | N | Some lectures will be dedicated to solve excercises with the aid of the computer. These will be a mix between basic exercises, and more realistic excercises and applications. The software used will be MATLAB. | |
| Formative Assessment [ON-SITE] | Assessment tests | CB02 CB03 CB04 CB05 CEB01 CG04 CT02 CT03 | 0.2 | 5 | Y | Y | The skill solving problems, the understanding of the theory and the proficiency with MATLAB will be evaluated through different tasks, as specified in section 8, "Evaluation Criteria and Grading System". | |
| Study and Exam Preparation [OFF-SITE] | Self-study | CB05 CEB01 CG03 CG04 CT03 | 3.6 | 90 | N | N | The student must work on its own, studying and understanding the theory and solving excercises. In this process they can relay on MATLAB, and should do so in order to train in the use of the software. | |
| Total: | 6 | 150 | ||||||
| Total credits of in-class work: 2.4 | Total class time hours: 60 | |||||||
| Total credits of out of class work: 3.6 | Total hours of out of class work: 90 | |||||||
As: Assessable training activity Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).
8. Evaluation criteria and Grading System
| Evaluation System | Continuous assessment | Non-continuous evaluation * | Description |
| Final test | 70.00% | 90.00% | There will be an exam consisting of both theoretical questions and exercises. For the studintes graded on the coniuous assesment system, the exam will consist only of excercises. The minimum grade in this activity, in order for it to be compensable, is 3.5 over 10. |
| Laboratory sessions | 10.00% | 10.00% | There will be an exam consisting of excercises that must be solved using MATLAB. The minimum grade in this activity, in order for it to be compensable, is 4 over 10. |
| Projects | 20.00% | 0.00% | The student must hand in the proposed exercises and questions in the dates specified at the begining of te course. The goal of this activity is to encourage the implication of the student with the subject throught the whole course. |
| Total: | 100.00% | 100.00% |
According to art. 4 of the UCLM Student Evaluation Regulations, it must be provided to students who cannot regularly attend face-to-face training activities the passing of the subject, having the right (art. 12.2) to be globally graded, in 2 annual calls per subject , an ordinary and an extraordinary one (evaluating 100% of the competences).
Evaluation criteria for the final exam:
-
Continuous assessment:Let TR, PF and ML be the grade attained respectively in the Projects, Final Test and Laboratory sessions activities. Then the final grade of the course, NF, is computed as:
NF = 0.2 * TR + 0.7 * PF + 0.1 *ML,
with the following considerations:
- Depending on the average grade of TR an ML, the student may opt to switch from the continuious assessment grading system to the non-continuous evaluation.
- If PR < 3.5, NF can be at most 4, regardless of the outcome of the previous formula, and therefore the student cannot pass the course.
- If ML < 4, NF can be at most 4, regardless of the outcome of the previous formula, and therefore the student cannot pass the course. -
Non-continuous evaluation:Let PF and ML be the grade attained respectively in the Final Test and Laboratory sessions activities. Then the final grade of the course, NF, is computed as:
NF = 0.9 * PF + 0.1 *ML,
with the following considerations:
- If ML < 4, NF can be at most 4, regardless of the outcome of the previous formula, and therefore the student cannot pass the course.
Specifications for the resit/retake exam:
There will an exam consisting of two parts: a first one with theoretical questions and excercises and a second one consisting on exercises to be solved with MATLAB.
If a student achieved a grade in one of the evaluation activities that made it compensable, they may keep that grade for the retake exam.
If a student has more than one grade in any activity, the larger of the two will be used.
If the grade corresponding to the lab sessions is smaller than 4 over 10, the final grade will be at most 4, and therefore the student cannot pass the course.
If a student achieved a grade in one of the evaluation activities that made it compensable, they may keep that grade for the retake exam.
If a student has more than one grade in any activity, the larger of the two will be used.
If the grade corresponding to the lab sessions is smaller than 4 over 10, the final grade will be at most 4, and therefore the student cannot pass the course.
Specifications for the second resit / retake exam:
There will an exam consisting of two parts: a first one with theoretical questions and excercises and a second one consisting on exercises to be solved with MATLAB. The criteria will be the same as in the "Non-continuous evaluation" system.
9. Assignments, course calendar and important dates
| Not related to the syllabus/contents | |
|---|---|
| Hours | hours |
| Class Attendance (theory) [PRESENCIAL][Combination of methods] | 30 |
| Problem solving and/or case studies [PRESENCIAL][Combination of methods] | 15 |
| Class Attendance (practical) [PRESENCIAL][Practical or hands-on activities] | 10 |
| Formative Assessment [PRESENCIAL][Assessment tests] | 5 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 90 |
| Global activity | |
|---|---|
| Activities | hours |
10. Bibliography and Sources