ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Hours of tutorials: 3 Expository Class: 27 Interactive Classroom: 21 Total: 51
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Mathematics
Areas: Algebra, Geometry and Topology
Center Faculty of Biology
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
In this course, the general objective is that students learn to use some basic tools of linear algebra, differential and integral calculus and differential equations, to model and solve biotechnology problems.
Specifically, students will learn the basic concepts and techniques of linear algebra, with an instrumental orientation towards a career in biotechnology. There will be a brief review of matrix operations and a reminder of the properties of determinants that students already know in high school. We will also make a quick incursion into solving systems of linear equations, as a natural continuation of the knowledge already acquired by students in high school subjects. This approach will allow us to address the diagonalization and triangularization of matrices that we will illustrate with some examples from the field of the degree program.
The concepts of derivative, and indefinite and definite integral of a real function of a real variable will also be remembered, as well as the usual calculation procedures. Then the fundamentals of differential equations will be introduced, as well as some basic procedures to find and study their solutions. All of this will be applied to the resolution of specific problems related to biotechnology. Derivatives and definite integrals will be extended to several variables to conclude.
Learning outcomes:
- To be able to handle different concepts of linear algebra, including matrix and determinant.
- To understand the meaning and interest of diagonalization and triangularization of a matrix.
- To be able to derive real functions, both from one and several real variables.
- To be able to calculate primitives of a real function of a real variable. To be able to calculate the value of an integral defined by Barrow's rule.
- To be able to apply some methods of integration of differential equations.
- To be able to mathematically formulate and solve some problems of differential equations in the field of biotechnology.
Topic 1. Matrices and determinants. (1 week)
Topic 2. Systems of linear equations. (1 week)
Topic 3. Diagonalization and triangularization. (2 weeks)
Topic 4. Derivation of a real function. Higher order derivatives. (1 week)
Topic 5. Calculation of primitives of a real function of a real variable. (2 weeks)
Topic 6. The definite integral: Barrow's rule. (2 weeks)
Topic 7. Differential equations. Integration of differential equations. Applications. (3 weeks)
Topic 8. Partial derivatives. (1 week)
Topic 9. Multiple integration. (1 week)
Basic bibliography:
- Batschelet, E. (1978): Matemáticas básicas para biocientíficos, Madrid, Dossat.
- Hadeler, K. P. (1982): Matemáticas para biólogos, Barcelona, Reverté.
- Martínez Calvo, M. C. and Pérez de Vargas, A. (1993): Métodos matemáticos en biología, Madrid, Centro de Estudios Ramón Areces.
- Martínez Calvo, M. C. and Pérez de Vargas, A. (1995): Problemas de biomatemática, Madrid, Centro de Estudios Ramón Areces.
Complementary bibliography:
- Grossman, S. I. and Turner, J. E. (1974): Mathematics for the biological sciences, Londres, Macmillan.
- Valderrama Bonnet, M . J. (1995): Modelos matemáticos en las ciencias experimentales, Madrid, Pirámide.
- Valderrama Bonnet, M .J. (1989): Métodos matemáticos aplicados a las ciencias experimentales, Madrid, Pirámide.
- Taubes, C. F. (2008): Modeling differential equations in biology, Cambridge, Cambridge University Press.
• Knowledge/contents: Con01
• Abilities/skills: H/D01, H/D02, H/D03
• Competencies: Comp01, Comp03
The expository classes will basically consist of teaching given by the professor, dedicated to the presentation of theoretical content and the resolution of problems or exercises. Sometimes the model will be brought closer to the master class and in other classes greater student participation will be sought. Attending classes is essential to understand the subject.
The seminars in small groups will allow, in some cases, the acquisition of practical skills and, in others, they will serve for the immediate illustration of the theoretical-practical contents. Active participation of students is mandatory.
The (individual or group) tutorials will serve to clarify doubts, provide information and guide the students, as well as to know the progress in the acquisition of skills.
The laboratories will be dedicated mainly to solving exercises and problems, as close as possible to applications to biotechnology. The exercises and problems will be proposed in advance, and students must solve them and learn how to explain and write the correct solutions, highlighting the essential ideas and techniques that are applied.
The evaluation system aims to evaluate the knowledge/contents, skills/abilities and competencies planned in the verification report.
Throughout the course, students must attend classes and solve exercises corresponding to each of the topics and actively participate in seminar classes, tutorials and laboratories. Special value will be given to the development of the ability to apply the explained techniques to solve real practical biotechnology problems. A positive attitude in class (interest in learning and facilitating the learning of others) will also be taken into account. If participation in solving the exercises is not satisfactory, written theoretical-practical tests for continuous evaluation may be carried out throughout the semester.
The joint score of these continuous evaluation activities will represent 30% of the final grade. The remaining 70% will come from the final exam. This exam will be written and may contain theoretical questions, theoretical-practical questions and exercises, but the majority of the exam will consist of practical exercises on applications related to biotechnology.
Repeating students will have the same evaluation system as students enrolled for the first time.
Evaluation of knowledge/contents, abilities/skills and competencies:
• Exam: Con01, H/D01, H/D02, Comp01.
• Oral and written participation in tutorials, seminars and laboratories: Con01, H/D01, H/D02, H/D03, Comp01, Comp03.
• Possible written tests for continuous evaluation: Con01, H/D01, H/D02, H/D03, Comp01, Comp03.
In addition to master classes (27 hours), seminars (17 hours), interactive classes (4 hours) and individual or small group tutorials (3 hours), the student must take the exam and dedicate 96 hours of personal work to theoretical study and resolution of exercises.
It is expected that students will attend classes regularly and
engage in individual or collective work on all topics covered in class.
Should difficulties arise, students are encouraged to utilice the tutorial system.
Jesús Antonio Álvarez López
Coordinador/a- Department
- Mathematics
- Area
- Geometry and Topology
- Phone
- 881813149
- jesus.alvarez [at] usc.es
- Category
- Professor: University Professor
Ana Jeremías López
- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813366
- ana.jeremias [at] usc.es
- Category
- Professor: University Lecturer
Angel Cidre Diaz
- Department
- Mathematics
- Area
- Geometry and Topology
- angel.cidre.diaz [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 11:00-12:00 | Grupo /CLE_01 | Galician, Spanish | Classroom 01. Charles Darwin |
| Tuesday | |||
| 11:00-12:00 | Grupo /CLE_01 | Spanish, Galician | Classroom 01. Charles Darwin |
| Thursday | |||
| 12:00-13:00 | Grupo /CLIS_01 | Galician, Spanish | Classroom 05 (video-conference). Rita Levi Montalcini |
| 13:00-14:00 | Grupo /CLIS_02 | Spanish, Galician | Classroom 06. Diane Fosey and Jane Goodall |
| Friday | |||
| 12:00-13:00 | Grupo /CLIS_01 | Galician, Spanish | Classroom 05 (video-conference). Rita Levi Montalcini |
| 13:00-14:00 | Grupo /CLIS_02 | Galician, Spanish | Classroom 06. Diane Fosey and Jane Goodall |
| 01.23.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 04: James Watson and Francis Crick |
| 06.27.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 03. Carl Linnaeus |