424 - Bachelor's Degree in Mechatronic Engineering
28810 - Mathematics III
28810 - Mathematics III
Faculty / School:
175 - Escuela Universitaria Politécnica de La Almunia
424 - Bachelor's Degree in Mechatronic Engineering
1.1. Aims of the course
Differential equations are a key element of modern mathematics. They constitute a solid ground for analysis, modeling and problem solving in diverse fields such as Engineering, Physical Sciences, Economics or Business.
An outstanding learning goal of the course is the mastery of practical and theoretical techniques which can be directly applied to realistic problem solving, using efficient and reliable computational software tools. It is therefore of utmost importance in the training of an engineer/officer to acquire this course's learning goals.
This course belongs to the basic education module. It addresses the ability to solve mathematical problems which can arise in Engineering. The basic education module provides working knowledge of linear algebra, geometry, differential geometry, differential and integral calculus, ordinary and partial differential equations, numerical methods and algorithms, statistics and optimization. All these subjects are covered by the courses Mathematics I, Mathematics II, Mathematics III and Statistics.
Mathematics III is a 6 ECTS credit compulsory course to be taken in the first semester, second year of the degree.
1.2. Context and importance of this course in the degree
The Mathematics III course is taken during the first semester of the second year of the Bachelor's Degree in Mechatronic Engineering.
This course aims to entitle students to pursue another scientific courses featuring mathematics, and prominently differential equations, as basic background. The topics covered in this course have direct applications in Physics, Mechanics, Electronics, Statistics and Economy. The language, critical thinking and reasoning which are inherent to Mathematics will help the students to understand the aforementioned courses.
1.3. Recommendations to take this course
The recommended profile to take Mathematics III is to possess the knowledge and skills acquired in previous subjects of the degree as Mathematics I and II.
In order to follow this subject correctly, it is also necessary to have a willingness to carry out a continuous work and effort from the beginning of the course. It is also advisable for students to resolve its doubts as they arise using classroom, tutorials as well as resources that the teachers make available.
In passing this subject, the student will be compentent in:
- GI03 - Knowledge of basic technological areas leading to learning new methods and theories, and providing the versatility needed to adapt oneself to new environments.
- GI04 - Ability to solve problems and take decisions with initiative, creativity and critical reasoning. Ability to communicate and transmit knowledge and skills in engineering.
- GC02 - Ability to interpret experimental data, compare them with theoretical models and draw conclusions.
- GC03 - Ability to use abstraction and logical reasoning.
- GC04 - Ability to continue learning and develop self-learning strategies.
- GC05 - Ability to evaluate alternatives.
- GC07 - Ability to lead a team as well as being a committed team member.
- GC08 - Ability to locate, comprehend and assess technical information.
- GC10 - Ability to prepare technical documentation and presentations with the help of appropriate software tools.
- GC11 - Ability to communicate thoughts and designs in a clear manner to specialist and non-specialist audience.
- EB01 - Ability to solve mathematical problems in engineering. Ability to apply knowledge about differential equations, integral and discrete transforms, and related numerical methods and algorithmics.
2.2. Learning goals
The student, in order to pass this subject, will have to achieve the following goals…
- He/she knows how to apply the main results about ODEs and PDEs as well as the numerical methods solving problems from the aforementioned disciplines.
- He/she develops and experiments problem solving strategies and is able to distinguish the most appropriate method in each case.
- He/she is able to reason the difficulty of solving a problem in an exact way and the necessity to apply numerical approximation methods to solve it, determining the degree of precision and the error made.
- He/she knows how to use a symbolic calculator applied to ODEs and PDEs, integral and discrete transforms.
- He/she is able to pose and rigorously solve problems in the previous areas applied to Mechatronic Engineering, choosing the most appropriate methods and theoretical results and, in the view of the complexity of solving these real problems analytically, he/she is able to solve them using the software from point 4.
- He/she is able to solve, working in team, the problems from point 5 widening the information and the methods presented during the classes. He/she is, in addition, able to perform oral presentations of the obtained results using the appropriate mathematical language and the more convenient software.
- He/she is able to express, both in oral and written form, and using scientific language, the basic facts of the subject and the process of problem solving.
2.3. Importance of learning goals
The obtained learning outcomes are important because they provide the students mathematical and procedural knowledge. These are in the basis of other scientific and technological subjects of the degree like, for instance, Physics, Mechanics, Operations research, Economics, Electronics, and Materials resistance. The ability to apply mathematical techniques to solve specific problems of different engineering-related fields is a core competence of an engineer, as well as how to use available resources and how to interpret the solutions.
3. Assessment (1st and 2nd call)
4. Methodology, learning tasks, syllabus and resources
4.1. Methodological overview
The learning process designed for this subject is based on the following:
Strong interaction between the teacher/student. This interaction is brought into being through a division of work and responsibilities between the students and the teacher. Nevertheless, it must be taken into account that, to a certain degree, students can set their learning pace based on their own needs and availability, following the guidelines set by the teacher.
The current subject is conceived as a stand-alone combination of contents, yet organized into three fundamental and complementary forms, which are: the theoretical concepts of each teaching unit, the solving of problems or resolution of questions, at the same time supported by other activities.
The organization of teaching will be carried out using the following steps:
- Lectures: Theoretical activities carried out mainly through exposition by the teacher, where the theoretical supports of the subject are displayed, highlighting the fundamental, structuring them in topics and or sections, interrelating them.
- Practice Sessions: The teacher resolves practical problems or cases for demonstrative purposes. This type of teaching complements the theory shown in the lectures with practical aspects.
- Individual Tutorials: Those carried out giving individual, personalized attention with a teacher from the department. Said tutorials may be in person or online.
4.2. Learning tasks
The course includes the following learning tasks:
Involves the active participation of the student, in a way that the results achieved in the learning process are developed, not taking away from those already set out, the activities are the following:
- Face-to-face generic activities:
- Lectures: The theoretical concepts of the subject are explained and illustrative examples are developed as a support to the theory when necessary.
- Practice Sessions: Problems and practical cases are carried out, complementary to the theoretical concepts studied.
- Generic non-class activities:
- Study and understanding of the theory taught in the lectures.
- Understanding and assimilation of the problems and practical cases solved in the practical classes.
- Preparation of seminars, solutions to proposed problems, etc.
- Preparation of the written tests for continuous assessment and final exams.
The subject has 6 ECTS credits, which represents 150 hours of student work in the subject during the trimester, in other words, 10 hours per week for 15 weeks of class.
The course will address the following topics:
- Ordinary Differential Equations: basic concepts, existence and uniqueness.
- Analytic solvability.
- Qualitative aspects: fixed points and linear stability.
- Numerical methods: Euler, Runge–Kutta.
- Higher orden ODE: Oscillators; resonance. Beam stability.
- Higher order numerical methods (FDM y FEM).
- Introduction to Partial Differential Equations: separation of variables; vibrations.
- Laplace Transform.
- Laplace Transform Applications.
- Discrete-time systems.
- The Z Transform.
- Z Transform Applications.
- Fourier Series and Fourier Transform.
- Applications of Fourier Series and Transforms.
- Discrete Time Fourier Transform: FFT and Applications.
4.4. Course planning and calendar
The dates of the final exams will be those that are officially published at https://eupla.unizar.es/asuntosacademicos/examenes.
||ODE: Introduction, 1st order
||Linear equation, Systems
||ODE 1st order
||2nd order ODE
||Signals and systems
||Fourier Series and Transform
||Separation of variables